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A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming that the involved parameters have a finite degree of randomness. The resulting mathematical model becomes a random free boundary partial differential problem and it is addressed numerically combining the finite difference method with two approaches for the treatment of the moving front. Firstly, we propose a front-fixing transformation, reshaping the original random free boundary domain into a fixed deterministic one. A second approach is using the front-tracking method to capture the evolution of the moving front adapted to the random framework. Statistical moments of the approximating solution stochastic process and the stochastic moving boundary solution are calculated by the Monte Carlo technique. Qualitative numerical analysis establishes the stability and positivity conditions. Numerical examples are provided to compare both approaches, study the spreading-vanishing dichotomy, prove qualitative properties of the schemes and show the numerical convergence. [ABSTRACT FROM AUTHOR]

This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize electrostatic forces to actuate elastic surfaces. The potential equilibrium states of MEMS are described by solutions of a singularly perturbed elliptic nonlinear PDE. We develop a numerical method which couples a finite element approximation with mesh refinement to a pseudo arc-length continuation algorithm to numerically obtain bifurcation diagrams in the physically relevant two dimensional scenario. Several geometries, including a unit disk, square, and annulus, are studied to understand the behavior of the system over a range of domains and parameter regimes. We find that solution multiplicity, and importantly the potential for bistability in the system, depends sensitively on the parameters. In the annulus domain, symmetry breaking bifurcations are located and asymmetric solution branches are tracked. This work significantly extends the envelope for numerical characterization of equilibrium states in microscopic electrostatic contact problems relating to MEMS. [ABSTRACT FROM AUTHOR]

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R 0 Δ x , is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we propose an effective Chebyshev–Picard iteration (CPI) method for solving delay differential equations with a constant delay. This approach adopts the Chebyshev series to represent the solution and improves the accuracy of the solution by successive Picard iterations. The CPI method is implemented in a matrix–vector form efficiently without matrix inversion. We also present a multi-interval CPI method for solving long-term simulation problems. Further, the convergence of the CPI method is analyzed by evaluating the eigenvalues of the coefficient matrices of the iteration. Several numerical experiments including both the linear and nonlinear systems with delay effects are presented to demonstrate the high accuracy and efficiency of the CPI method by comparison with the classic methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel COVID-19 reaction–diffusion model with virus mutation and media coverage is investigated. First, the solution's uniform boundedness for the system is established. Then, the basic reproduction numbers for ordinary and mutant viruses spread in heterogeneous environments are defined. Furthermore, the endemic equilibrium's asymptotic distribution for the system is explored. In addition, when one diffusion coefficient tends to zero and the other diffusion coefficients are greater than zero and fixed, the solution of the system will asymptotically approach endemic equilibrium. Next, a theoretical analysis of how high-frequency media coverage affects the development of the COVID-19 epidemic is conducted. Theoretical research shows that high-frequency media coverage will lead to the disappearance of the disease. Meantime, global sensitivity analysis on the basic reproduction numbers R 01 and R 02 are performed. Finally, theoretical simulations and instance predictions are carried out. Because of the complexity of the Shanghai epidemic and changes in management and control, the infection rates β 1 (t) , β 2 (t) are given in the form of a piecewise function with more practical significance, and they are used to predict the epidemic trend of COVID-19 in Shanghai. Through a series of numerical simulations and analysis, the key indicators of the Shanghai COVID-19 epidemic are as follows : (1) The basic reproduction numbers in the early, middle, and late stages of COVID-19 are R ¯ 0 (1 : 34) = 0. 9152 , R ¯ 0 (35 : 49) = 3. 1476 , and R ¯ 0 (50 : 140) = 0. 6547 , respectively; (2) This epidemic round in Shanghai will peak at 3,270 new daily confirmed cases on the 49th day (April 15); (3) The final size of the epidemic will reach 63,470 confirmed cases; (4) This round of COVID-19 epidemic in Shanghai, China, is expected to be fully cleared in late June to early July. The above conclusions are basically consistent with the facts. Of course, with the rise in temperature and strict control, the epidemic situation in Shanghai, China, is expected to be cleared earlier. Our results provide new ideas for preventing and controlling the COVID-19 epidemic. • A reaction–diffusion model with virus mutation and media coverage is proposed. • The asymptotic properties of endemic equilibrium with small diffusion are explored. • Global sensitivity analysis for R 01 and R 02 and are performed. • Applying piecewise functions β 1 (t) , β 2 (t) , to predict the Shanghai COVID-19 epidemic. • Key indicators of COVID-19, such as R 0 , peak, final scale, clear time are obtained. [ABSTRACT FROM AUTHOR]

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant ɛ ∈ (0 , 1 ] , we proposed a time-splitting Fourier pseudo-spectral (TSFP) scheme by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through rigorous error analysis, we establish improved error bounds for the scheme at O (h m + ɛ τ 2) up to the long time at O (1 / ɛ) where h is the mesh size and τ is the time step, respectively, and m depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGSE with the small coupling constant. The tools for error analysis mainly include the mathematical induction and the standard energy method as well as the regularity compensation oscillation (RCO) technique which has been developed recently. The numerical experiments support our theoretical analysis. Our scheme is novel because that to the best of our knowledge there has not been any TSFP scheme and any relevant long time analysis for the KGSE. [ABSTRACT FROM AUTHOR]

The price of a barrier option is often computed numerically. Due to the path dependency, the convergence rate of such numerical approximation is generally of order 1 / 2. In this paper, we show that the convergence order can be achieved at 1 under certain condition. This confirms a numerical analysis done previously by the third author with others. We consider the case where the underlying process is a Brownian motion with drift. The price of a barrier option coincides with the price of a vanilla option of the "symmetrized" diffusion, which has a discontinuous drift. The symmetrized diffusion is then approximated by a Markov chain and the corresponding option price is calculated. This approximation to the barrier option is shown to have a convergence order of 1 under some mild condition on the initial value of the process and the payoff function. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical positivity, convergence and dynamical behaviors (including extinction and persistence) for stochastic SIR model. For the real significance of the numerical analysis on stochastic SIR model, a linearly implicit Euler method with truncated Wiener process is introduced. The numerical positivity is obtained by the truncated Wiener process, which is the basis for the investigation of convergence and dynamical behavior. The numerical dynamical behavior is obtained by an exponential presentation for the nonlinear stochastic stability function and the large number theorem for martingale, which reproduces the existing theoretical results of exact solution. Finally, numerical examples are given to validate our numerical results for stochastic SIR model. [ABSTRACT FROM AUTHOR]

Time-varying problems frequently arise in the territories of science and engineering, and most of the time-varying problems can be described by dynamic matrix equations. As a powerful tool for solving dynamic matrix equations, the zeroing neural network (ZNN) develops fast in recent years. Convergence and robustness are two main performance indicators of the ZNN model. However, the development of the ZNN is focused on the improvement of its convergence in the past, and its robustness to noises is rarely considered. In order to achieve fast convergence and robustness of the ZNN model, a novel activation function (NAF) is presented in this paper. Based on the NAF, a noise-tolerant parameter-variable ZNN (NTPVZNN) model for solving dynamic Sylvester matrix equations (DSME) is realized, and its fixed-time convergence and robustness to noises are verified by rigorous mathematical analysis and numerical simulation results. Besides, two examples of electrical circuit currents computing and robotic manipulator trajectory tracking using the proposed NTPVZNN model in noisy environment further demonstrates its practical application ability. [ABSTRACT FROM AUTHOR]

In this paper, we focus on develop high-order and structure-preserving numerical algorithm for the two-dimensional nonlinear space fractional Schrödinger equations. By constructing a new generating function, we obtain a fourth-order numerical differential formula and use it to approximate the spatial Riesz derivative, while the Crank–Nicolson method is applied for the time derivative. Based on the energy method, the conservation, solvability and convergence of the numerical algorithm are proved. Finally, some numerical examples are used to verify the correctness of the theoretical analysis and the validity of the numerical algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a kinetic equation of Euler–Bernoulli beam is established with variable order fractional viscoelastic model. An effective numerical algorithm is proposed. This method uses a combination of shifted Bernstein polynomial and Legendre polynomial to approximate the numerical solution. The effectiveness of the algorithm is tested and verified by mathematical examples. The dynamic behavior of viscoelastic beams made of two materials under various loading conditions is studied. [ABSTRACT FROM AUTHOR]

As the backbone of social development, college students' level of physical exercise has always been the focus of research by experts and scholars. Most of the research methods are on the strength of literature data, questionnaire survey, mathematical statistics and comparative analysis. Based on the classification of college students and the influence and flow law of inter-class population, this paper establishes a differential equation system. By analyzing the existence and stability of the equilibrium of this system and the possible fold or backward bifurcations at the equilibrium, the quantitative analysis of college students' physical exercise trends on campus is carried out. This paper aims to improve the participation of college students in physical exercise by maximizing the number of students in the third categories. The results of theoretical proof, sensitivity analysis and numerical simulation show that in the initial stage, promoting peer-to-peer communication is the most effective measure. Secondly, when the effect of peer-to-peer interaction reaches saturation point, the way to improve physical education can achieve significant results. To fundamentally improve the enthusiasm of college students to participate in sports activities, we should start from the level of consciousness and enhance students' awareness of physical exercise from an early age. [ABSTRACT FROM AUTHOR]

An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]

This paper is devoted to the rigorous derivation of some discrete versions of stochastic Grönwall inequalities involving a martingale, which are commonly used in the numerical analysis of multi-term stochastic time-fractional diffusion equations. A Grönwall lemma is also established to deal with the numerical analysis of multi-term stochastic fractional diffusion equations with delay. The proofs of the established inequalities are based on a corresponding deterministic version of the discrete fractional Grönwall lemma in case of smooth solutions and an inequality bounding the supremum in terms of the infimum for discrete time martingales. A numerical application is introduced finally in which the constructed inequalities are handled to derive a priori estimates for a discrete fractional stochastic model. [ABSTRACT FROM AUTHOR]

We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf–sup stable finite elements have been found suitable to avoid spurious pressure oscillations in the initial phase of the evolution. In this paper, we first clarify the role of the inf–sup condition for the well-posedness of the continuous problem and discuss the choice of appropriate initial conditions. We then develop an abstract error analysis that allows us to analyse some approximation schemes discussed in the literature in a unified manner. In addition, we propose and analyse the high-order time discretization by a scheme that can be interpreted as a variant of continuous-Galerkin or particular Runge–Kutta methods applied to a modified system. The scheme is designed to preserve both, the underlying differential–algebraic structure and the energy-dissipation property of the problem. In summary, we obtain high-order Galerkin approximations with respect to space and time and derive order-optimal convergence rates. The numerical analysis is carried out in detail for the discretization of the two-field formulation by Taylor–Hood elements and a variant of a Runge–Kutta time discretization. [ABSTRACT FROM AUTHOR]

Advanced numerical analysis of structures forces the massive implementation of numerical algorithms, relying on certain convergence of sequences of discrete finite element and similar approximations in spaces of integrable functions, conceding non-physical discontinuities and imperfectness to all numerical results. This is demonstrated on a model example of a thick elastic beam on the 2-parametric Pasternak subsoil. A potential remedy, discussed in this paper, comes from the implementation of available knowledge of analytical solutions in standard variational formulations. The resulting sparse system of linear algebraic equations can be derived without any numerical differentiation; the numerical quadrature is limited to some integrals of explicitly known (MAPLE-generated) functions. Potential generalizations, including selected nonlinear problems, are sketched. [ABSTRACT FROM AUTHOR]

American options prices under jump–diffusion models are determined by a free boundary partial integro-differential equation (PIDE) problem. In this paper, we propose a front-fixing exponential time differencing (FF-ETD) method composed of several steps. First, the free boundary is included into equation by applying the front-fixing transformation. Second, the resulting nonlinear PIDE is semi-discretized, that leads to a system of ordinary differential equations (ODEs). Third, a numerical solution of the system is constructed by using exponential time differencing (ETD) method and matrix quadrature rules. Finally, numerical analysis is provided to establish empirical stability conditions on step sizes. Numerical results show the efficiency and competitiveness of the FF-ETD method. [ABSTRACT FROM AUTHOR]

In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series of suitable Lyapunov functions and using some differential inequality techniques, the long-time asymptotic properties of the stochastic delayed system are investigated. These properties reveal that the solution of the stochastic system oscillates around the equilibrium points of the deterministic system when the intensity of environmental perturbations is appropriate. In addition, the sufficient condition for persistence in mean and extinction of the stochastic system are established under the suitable condition. At last, numerous numerical simulations show that the HIV will disappear if the intensity of environmental fluctuations is sufficiently large. This means that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV. • A stochastic delay HIV system with humoral immunity is proposed. • Asymptotic properties,persistence in mean and extinction, are investigated. • A series of Lyapunov functions and differential inequality are constructed and used. • Numerical simulations confirmed the effects of stochastic fluctuations on HIV. • Stochastic fluctuations can effectively suppress the outbreak of HIV. [ABSTRACT FROM AUTHOR]

This paper investigates a dual-channel supply chain (SC) composed of a manufacturer and retailer in which the manufacturer confronts random yield issues. Since supply uncertainty may lead to a production shortage, the manufacturer faces the problem of allocating the products to traditional/online channels. To address this problem, a novel product-allocation policy is developed in which the limited supply is allocated to traditional and online channels under a flexible strategy called "targeted capacity allocation". In order to coordinate the proposed decentralized channel, a two-part tariff contract is suggested. Furthermore, opening a direct channel besides brick-and-mortar stores is discussed through analytical results. Then, the effectiveness of the targeted capacity allocation policy is investigated by comparing the results of the current model with a case, in which, the same policy is not applied. By doing so, some interesting managerial insights on the merit of applying the capacity allocation policy in managing dual-channel SCs under yield uncertainty are revealed. Finally, numerical analysis shows that the proposed contract can perfectly coordinate the SC and achieve the Pareto improving solution for both partners. [ABSTRACT FROM AUTHOR]

Based on a new robust zeroing neural network (RZNN) model, the trajectory tracking control of a wheeled mobile robot (WMR) within fixed-time in noise-polluted environment is presented in this paper. Unlike most of the previous reported works, the RZNN model approach for trajectory tracking control of the WMR reaches fixed-time convergence and noise suppression simultaneously. Besides, detailed theoretical analysis of its convergence and robustness are provided. Numerical simulation verification is also provided to demonstrate the superior robustness and accurateness of the RZNN model approach for trajectory tracking control of the WMR in noise-polluted environment. Both of the theoretical analysis and numerical simulation results verify the effectiveness and robustness of the RZNN model approach. [ABSTRACT FROM AUTHOR]

Abstract It is well-known that the quality of random number generators can often be improved by combining several generators, e.g. by summing or subtracting their results. In this paper we investigate the ratio of two random number generators as an alternative approach: the smaller of two input random numbers is divided by the larger, resulting in a rational number from [ 0 , 1 ]. We investigate some basic theoretical properties of this approach and show that it yields a good approximation to the ideal uniform distribution. The focus of this paper, however, is on the empirical performance of the new transformation when applied to different generators. For a thorough statistical evaluation, we use the well-known test suite TestU01 (see L'Ecuyer and Simard, 2007). We apply the ratio transformation to moderately bad generators, i.e. those that failed up to 40% of the tests from the test battery Crush of TestU01. We show that more than half of them turn into empirically very good generators that pass all tests of Crush and BigCrush from TestU01 when the ratio transformation is applied. In particular, generators based on linear operations seem to benefit from the ratio, as this breaks up some of the unwanted regularities in the input sequences. Thus the additional effort to produce a second random number and to calculate the ratio allows to increase the quality of available random number generators, at least in a statistical sense. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fully discretization scheme for infinite age-structured population models with time-variable fertility rate and mortality rate. Based on the characteristics, the classical linear θ -methods with a kind of two-layer boundary condition are constructed for preserving an invariance of total populations. We are interested in the finite-time convergence and the stability for a long time. With the classical approach, some conjecture on the first order convergence is proved. For the time-independent model the numerical stability is studied by an embedded infinite dimensional dynamical system, which provides a numerical basic reproduction number by the infinite Leslie operator. Furthermore, it is shown that the numerical solutions replicate the un-stability and stability of the analytical solutions for small stepsize. Finally, three examples are given to verify the feasibility of our methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fractional Biswas–Milovic model having Kerr and parabolic law nonlinearities via the application of fractional complex transform (FCT) coupled with the homotopy perturbation transform technique (HPTT). HPTT is a fusion of homotopy perturbation method with Laplace transform The obtained numerical results are demonstrated through graphs and tables. The numerical simulation results assure the reliability of the proposed technique with less computational time and high accuracy of the results. Also, comparative simulation studies have been performed to show that the proposed technique provides better approximations than the residual power series method (RPSM). • The compilation of fractional complex transform with homotopy perturbation approach is suggested. • The fractional Biswas–Milovic model having Kerr and parabolic law nonlinearities is investigated. • Real and imaginary division of the wave profile are presented separately along with the contour plots. • Comparative simulation studies have been performed, L 2 and L ∞ error norms are also presented in tables. • Good agreement with exact solution is obtained. [ABSTRACT FROM AUTHOR]

In this paper we investigate the dynamic behavior and the numerical analysis for a thermoelastic diffusion problem in one space dimension with moving boundary. Global existence is proved by using the penalty method of Lions and the Galerkin approximations. Under suitable conditions, we prove that the energy functional decays to zero as the time tends to infinity by the method of perturbation energy. An uncoupled numerical method was developed to obtain an approximate numerical solution with order of quadratic convergence in time and space. Tables and graphs of the approximate solution are displayed for a copper like material, to verify the efficiency and feasibility of the proposed method. Furthermore, we show that the numerical results are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel potential energy regeneration system (PERS) using a hydraulic accumulator and a valve–motor–generator for a hybrid hydraulic excavator (HHE). To analyze the dynamic performance of the proposed PERS, mathematical models are established. A numerical analysis is conducted to guide the parameters design of the key components in the PERS. The control strategy for the energy regeneration system (ERS) is discussed. Simulations are carried out in AMESim to validate the effectiveness of the novel PERS. The results demonstrate that the dynamic performance of the PERS is close to that of a throttle-governing system. The efficiency of the PERS is about 58%. Highlights • A novel PERS using a valve–motor–generator and a hydraulic accumulator, is put forward for HHE. • Mathematical models are constructed to analyze the dynamic performance of the PERS. • Parameters of key components in the PERS are designed according to actual working conditions. • The dynamic performance of the PERS is close to that of the throttle governing system. • The efficiency of the PERS is about 58%. [ABSTRACT FROM AUTHOR]

This paper presents several numerical techniques to generate solitary-wave profiles of the Benjamin equation. The formulation and implementation of the methods focus on some specific points of the problem: on the one hand, the approximation of the nonlocal term is accomplished by Fourier techniques, which determine the spatial discretization used in the experiments. On the other hand, in the numerical continuation procedure suggested by the derivation of the model and already discussed in the literature, several algorithms for solving the nonlinear systems are described and implemented: the Petviashvili method, the Preconditioned Conjugate Gradient Newton method and two Squared-Operator methods. A comparative study of these algorithms is made in the case of the Benjamin equation; Newton's method combined with Preconditioned Conjugate Gradient techniques, emerges as the most efficient. The resulting numerical profiles are shown to have a high accuracy as travelling-wave solutions when they are used as initial conditions in a time-stepping procedure for the Benjamin equation. The paper also explores the generation of multi-pulse solitary waves. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider the issues for increasing computation schemes performance while modelling non-isothermal convective diffusion using Caputo fractional derivative model. We propose to solve the considered problem using locally one-dimensional finite difference scheme. As the numerical computation of fractional derivative has the biggest influence on computational complexity, an additional approximation procedure of logarithmic complexity is proposed. The procedure represents finite difference form of the fractional derivative as two sets of partial Taylor series which are modified in the process of sequential computations during modelling. As the considered model is non-isothermal, two coupled processes of different speeds are considered. In this case the use of non-uniform time steps can be efficient to improve performance. The proposed approximation procedure is modified for the case of non-uniform time steps and the trial and error method is used to dynamically change time step length during modelling. Time interval in which such schemes are efficient is experimentally determined. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we aim to compute numerical approximations of the integral of a function by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called indicators which indicate where the variance takes relative large values. The stratification method is based on the optimal allocation strategy in order to decrease the variance from one iteration to another. Numerical experiments show and confirm the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we introduce a new extension to the extreme value type-1 (Gumbel) distribution, by constructing a slash type distribution. The result is a distribution with greater kurtosis than the Gumbel distribution. Properties of the distribution such as moments, moment generating function and kurtosis and asymmetry coefficients for the distribution are studied. Maximum likelihood estimation and moments estimators are applied and a simulation study is presented to illustrate parameter recovery. Results of applications to two real data sets, one from a wind velocity study and the other from snow accumulation indicate that the new model seems to perform better in the presence of atypical observations. Highlights • An extension of the Gumbel model is presented. • This extension allows to obtain a bigger range to the kurtosis coefficient. • Euler's constant and the zeta and polygamma functions are related. • The parameter estimation was approached using the method of moments and the MLE. • Simulations and two real data sets show the good performance of this new model. [ABSTRACT FROM AUTHOR]

Abstract Zika virus epidemic poses a major threat to public health globally. Initially, this disease was limited to Africa but now it is spreading throughout the World. It is well known that zika virus is transmitted to human by the bites of Aedes mosquitoes. Recently, there are reported cases of sexual transmission and transmission due to blood transfusion in many countries e.g., Argentina, France, New Zealand, USA etc. In this paper a mathematical model of Zika virus on complex network is formulated and analyzed keeping in mind both mosquito-borne and sexual transmission of this disease. The existence and global stability of disease-free equilibrium are discussed in detail. The basic reproduction number R 0 of the model is computed and it is found that for R 0 < 1 , the disease-free equilibrium of the model is globally asymptotically stable under some condition. In addition to this the final size relation of the proposed model is also computed. The key parameters of the model are computed using curve fitting to the real data by least-square method. Sensitivity analysis and numerical simulation are also performed for our proposed model. Finally, this model is extended to optimal control problem, to find the suitable cost-effective and time-dependent control strategies to reduce the number of infectives in a desired interval of time. [ABSTRACT FROM AUTHOR]

Abstract The paper focuses on single and multiple current sensors fault detection and isolation (FDI) for induction motor (IM) drives using only two current sensors. Two model based diagnosis methods are proposed to estimate the current residuals dynamics in the stationary reference frame: The first one is a differential algebraic estimation of fault dynamics and the second one is based on a combination of the Robust Integral Sign of the Error (RISE) observer with the algebraic approach. After detecting the fault occurrence, a logic based decision unit is then built to identify the faulty sensors. The resulting residuals are robust to load torque disturbances. Moreover, the developed fault estimators are simple with a 1-D model, based only on the input–output measurements and their derivatives and do not require a bank of observers. Furthermore, the used residual threshold is well defined and is suitable for the whole operating range. The ability of diagnosing the recovery of a sensor from a fault is also demonstrated. The validity of the developed approaches is analytically proved and a comparative study is carried out between the two FDI schemes. [ABSTRACT FROM AUTHOR]

In this paper the ideas presented in the article Deolmi et al. (2017) to simulate efficiently a compressible flow over a rough surface are extended to a two-step model order reduction strategy. The first level consists in the formulation of effective boundary conditions, to take into account the effect of the roughness without resolving it. This requires the solution of a parameter-dependent cell problem on the micro-scale. To reduce its computational cost we add an additional step, where a second level of reduction is applied to the cell problem by means of the reduced basis method. Through numerical computations we verify the gain in efficiency of this strategy. [ABSTRACT FROM AUTHOR]

We consider Filippov sliding motion on a co-dimension 2 discontinuity surface. We give conditions under which Σ is attractive through sliding which are sharper than those given in a previous paper of ours. Under these sharper conditions, we show that the sliding vector field considered in the same paper is still uniquely defined and varies smoothly in x ∈ Σ . A numerical example illustrates our results. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical computation of the matrix p th root of stochastic matrices. In particular a collection of theoretical results concerning the p th root of stochastic matrices is reported and some numerical methods are described. The aim of the paper is to highlight the properties of such methods when they are applied to numerically compute the p th root of a stochastic matrix when it is expected to be stochastic too. [ABSTRACT FROM AUTHOR]

Abstract: The computations of likelihood or posterior distribution of parameters of complex population genetics models are common tasks in computational biology. The numerical results of these approaches are often found by Monte Carlo simulations. Much of the recent work of Monte Carlo approaches to population genetics problems has used pseudorandom sequences. This paper explores alternatives to these standard pseudorandom numbers and considers the use of uniform random sequences, more specifically, uniformly distributed sequences (quasi-random numbers) to calculate the likelihood. We demonstrate by examples that quasi-Monte Carlo can be a viable alternative to the Monte Carlo methods in population genetics. Analysis of a simple two-population problem in this paper shows that parallel quasi-Monte Carlo methods achieve the same or better parameter estimates as standard Monte Carlo and have the potential to converge faster and so reduce the computational burden. [Copyright &y& Elsevier]

For elastic registration, topology preservation is a necessary condition to be satisfied, especially for landmark-based image registration. In this paper, we focus on the topology preservation properties of two different families of radial basis functions (RBFs), known as Gneiting and Matérn functions. Firstly, we consider a small number of landmarks, dealing with the cases of one, two and four landmark matching; in all these situations we analyze topology preservation and compare numerical results with those obtained by Wendland functions. Secondly, we discuss the registration properties of these two families of functions, when we have a larger number of landmarks. Finally, we analyze the behavior of Gneiting and Matérn functions, considering some test examples known in the literature and a real application. [ABSTRACT FROM AUTHOR]

In this paper we suggest a modification of the regression-based variance reduction approach recently proposed in Belomestny et al. [1]. This modification is based on the stratification technique and allows for a further significant variance reduction. The performance of the proposed approach is illustrated by several numerical examples. [ABSTRACT FROM AUTHOR]

Based on two different spaces defined on one coarse grid with mesh size H and one fine grid with mesh size h , a two-grid finite volume method is introduced to obtain the solutions of semi-linear reaction–diffusion equations of the solutes in the groundwater flow. The standard finite element Ritz projection and elliptic projection are applied to the analysis of this approach. Error estimates in L 2 norm and H 1 norm are derived in this paper. The above estimates can be applied to choose H = O ( h 1 / 4 ) in the H 1 norm and H = O ( h 1 / 2 ) in the L 2 norm for the coarse grid problems. Some numerical examples are presented to justify the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

Adaptive computation is now recognized as essential for solving complex PDE problems. Conceptually, such a computation requires at each step the definition of a continuous metric field (mesh size and direction) to govern the generation of adapted meshes. In practice, in the adaptive computation, an appropriate a posteriori error estimation is used and an upper-bounding of the error is expressed in terms of discrete metrics associated with the element vertices. In order to obtain a continuous metric field, the discrete field is recovered in the whole domain mesh using an appropriate interpolation method on each element. In this paper, a new method for interpolating discrete metric fields, based on a so-called “natural decomposition” of metrics, is introduced. The proposed method uses known matrix decompositions and is computationally robust and efficient. Classical interpolation methods are recalled and, from numerical examples on simplicial mesh elements, some qualitative comparisons against the new methodology are made to show its relevance. [ABSTRACT FROM AUTHOR]

In this paper, we present a new technique to get superconvergence phenomenon of spline quasi-interpolants at the knots of the partition. This method gives rise to good approximation not only at these knots but also on the whole domain of definition. Moreover, we give an application to numerical integration. Numerical results are given to illustrate the theoretical ones. [ABSTRACT FROM AUTHOR]

Results in a recent paper, concerning a novel three-dimensional chaotic system consisting of a particular set of three autonomous first-order nonlinear ordinary differential equations, are quite extended. We report on numerically computed parameter plane plots for a six-parameter system. The dynamical behavior of each point is characterized by using Lyapunov exponents, or by counting the number of maxima of one of the variables, in one complete trajectory in the phase-space. Each of these diagrams indicates parameter values for which chaos or periodicity may be found, i.e. , each one of them shows delimited regions of both chaos and periodicity. Moreover, we show that several of these parameter planes display self-organized periodic structures, embedded in a chaotic region. [ABSTRACT FROM AUTHOR]

One of the distinguishing features of Isogeometric Analysis is the usage of the same function space for describing the global, pre-discretization domain of a partial differential equation and for approximating its solution. Quite often, however, the domain consists of several patches where each patch is parametrized by means of Non-Uniform Rational B-Splines (NURBS), and these patches are then glued together by means of continuity conditions. While techniques known from domain decomposition can be carried over to this situation, the analysis of shell structures is substantially more involved as additional angle preservation constraints between the patches might arise. In this paper, we address this issue in the stationary and transient case and make use of the analogy to constrained mechanical systems with joints and springs as interconnection elements. Starting point of our work is the bending strip method (Kiendl et al., 2010) which adds extra stiffness to the interface between adjacent patches and which is found to lead to a so-called stiff mechanical system that might suffer from ill-conditioning and severe step size restrictions during time integration. As a remedy, an alternative formulation is developed that improves the condition number of the system and removes the penalty parameter dependence. Moreover, we study another alternative formulation with continuity constraints applied to triples of control points at the interface. Numerical results show a comparison between the different formulations where we observe that the alternative formulations are well conditioned, independent of any penalty parameter and give the correct results. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new method for the simulation of the exit time and exit position of a δ -dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The method, called walk on moving spheres algorithm, was first introduced for hitting times of Bessel processes. In this study this method is adapted and developed for the first time for the Brownian motion hitting times. The idea is to use the connexion between the δ -dimensional Bessel process and the δ -dimensional Brownian motion thanks to an explicit Bessel hitting time distribution associated with a particular curved boundary. This allows to build a fast and accurate numerical scheme for approximating the hitting time. We introduce also an overview of existing methods for the simulation of the Brownian hitting time and perform numerical comparisons with existing methods. [ABSTRACT FROM AUTHOR]

In this paper we review recent discrepancy bounds for ( t , s ) -sequences and other low-discrepancy sequences. We then provide numerical comparisons of these bounds for various combinations of dimension and number of points. In some cases, we compare different bounds for the same type of construction, and in other cases, we compare the best bounds across different constructions. [ABSTRACT FROM AUTHOR]

Numerical simulations of high strain rate plastic flow have historically been built in a hypoelastic framework and use radial return (Wilkins’ method) as the solution algorithm. We show how each of these choices can lead to inaccurate and possibly nonconvergent results. We describe an alternative solution procedure based on a simple multiple time scale perturbation theory that is stable, accurate, computationally efficient and simple to implement. Further extension of these results then leads to a strain space formulation that has additional computational advantages. We illustrate our development with numerical experiments. This paper is dedicated to my friend and colleague Christo Christov on the occasion of his 60th birthday, in recognition of his many important and creative contributions to the formulation of continuum mechanics. [ABSTRACT FROM AUTHOR]

It is well known that a train of solitons can emerge from the harmonic initial wave in case of the Korteweg–de Vries (KdV) or KdV related evolution equations. Analysis of results of numerical experiments demonstrates that besides clearly visible solitons, which interact with each other, there exist also solitons that either are visible only for a short time due to the fluctuation of the reference level or can be detected only by their influence on other solitons, i.e., by specific changes in the amplitude curves and in the soliton trajectories. Recently I. Christov demonstrated that for integrable PDEs, like the KdV equation, one can apply the periodic inverse scattering transform (PIST) and distinguish “true” soliton modes and modes that fall “in-between” solitons and radiation. However, in nonintegrable cases one cannot apply the PIST and therefore distinction between “true” solitons and nonlinear waves that have solitonic behavior seems to be complicated or even impossible. The existence of hidden solitons in the KdV related systems is discussed in the present paper. [ABSTRACT FROM AUTHOR]

This paper, following Kaldor’s approach, is written with the intention of interpreting fluctuations of economic systems (i.e trade cycles). In particular, a new discretized Kaldor model is proposed, which is also useful to explain what appears to be random and unpredictable, such as economic shocks. Moreover, by using numerical analysis, the chaoticity of the model is demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, a parametric family including Newton’s and Traub’s iterative schemes is presented. Its local convergence and dynamical behavior on quadratic polynomials are studied. The analysis of fixed and critical points and the associated parameter plane show the dynamical richness of the family and allow us to find members of it with good numerical properties, as well as other ones with very unstable behavior. [ABSTRACT FROM AUTHOR]

In this paper, a comparison study of conservative Allen–Cahn and Cahn–Hilliard equations is presented. We consider two mass-conservative Allen–Cahn equations and two Cahn–Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations. [ABSTRACT FROM AUTHOR]