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In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe. [ABSTRACT FROM AUTHOR]

This paper deals with the approximations of the functions by generalized Durrmeyer operators of Szász–Mirakjan, which are linear positive operators. Several approximation results are presented well, and we estimate the approximation properties along with the order of approximation and the convergence theorem of the proposed operators. For an explicit explanation of the operators, we determine the properties using the weight function. A quantitative approach is discussed for the operators; quantitative Voronovskaya type and Grüss type theorems are established, showing the operators' more efficient work. We investigate the A$$ A $$‐statistical convergence properties for the said operators, including the rate of approximation in a statistical sense. An important property for the rate of convergence of the operators is obtained in terms of the function with a derivative of the bounded variation. At last, the graphical representations and numerical analysis are discussed and shown to support our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp‐estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of the global solution to the Fractional Hyperbolic Systems of Partial Differential equations (FHyPDifS) by the Caputo–Hadamard fractional‐order derivative. In addition, we give a new sufficient conditions for the finite time stability (FTS) of FHyPDifS for the Caputo–Hadamard fractional‐order derivative. Finally, a numerical example is presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a spatiotemporal reaction–diffusion model for epidemics to predict how the infection spreads in a given space. The model is based on a system of partial differential equations with the Neumann boundary conditions. First, we study the existence and uniqueness of the solution of the model using the semigroup theory and demonstrate the boundedness of solutions. Further, the proposed model's basic reproduction number is calculated using the eigenvalue problem. Moreover, the dynamic behavior of the disease‐free steady states of the model for R0<1$$ {\mathcal{R}}_0<1 $$ is investigated. The uniform persistence of the model is also discussed. In addition, the global asymptotic stability of the endemic steady state is examined. Finally, the numerical simulations validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an uncoupled and linearized compact finite difference scheme for the generalized dissipative symmetric regularized long‐wave (GDSRLW) equations. The unique solvability and some a priori estimates of the proposed difference scheme are rigorously proved based on the mathematical induction method. To obtain the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm estimation of numerical solutions, the discrete energy method is used to prove the convergence and stability of the difference scheme. The proposed difference scheme preserves the original energy dissipation property, and the convergence of the scheme is proved to be fourth‐order in space and second‐order in time in the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm for both u$$ u $$ and ρ$$ \rho $$. Some numerical experiments are given to verify the theoretical analysis and the reliability of the proposed difference scheme. [ABSTRACT FROM AUTHOR]

For all humanity, the sudden outbreak of Corona Virus Disease 2019 has been an important problem. Timely and effective media coverage is considered to be one of the effective approaches to control the spread of epidemic in early stage. In this paper, a Sentiment‐enabled Susceptible‐Exposed‐Infected‐Recovered (SEIR) model is established to reveal the relationship between the propagation of the epidemic and media coverage. The authors take the positive and negative media coverage into consideration when implementing the Sentiment‐enabled SEIR model. This model is constructed by parameterizing the number of current confirmed cases, cumulative cured cases, cumulative deaths, and media coverage. The numerical simulation and sensitivity analysis are conducted based on the Sentiment‐enabled SEIR model. The numerical analysis confirms the rationality of the Sentiment‐enabled SEIR model. The sensitivity analysis shows that positive media coverage acts a pivotal part in reducing the figure for confirmed cases. Negative media coverage has an effect on the figure for confirmed cases is not as significant as that of positive media coverage, but it is not negligible. [ABSTRACT FROM AUTHOR]

In this paper, a semi‐discrete rotational velocity‐correction projection method is proposed to solve the Kelvin–Voigt viscoelastic fluid equations. In this method, the rotational velocity‐correction projection method can preserve the divergence free of the velocity u$$ u $$, and the nonlinear equation was linearized. Then, the unconditional stability and optimal convergence order will be provided by the numerical analysis. Finally, our analysis are confirmed by some numerical results, and the algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper, a second‐order accurate scheme is considered for the temporal discretization of the abstract Volterra integrodifferential equation with a weakly singular kernel. The time discrete scheme is constructed by the Crank–Nicolson method for approximating the time derivative and product integration (PI) rule for approximating the integral term. The proposed scheme employs a graded mesh for time to compensate for the singular behavior of the exact solution at t=0$$ t&#x0003D;0 $$. Under the suitable assumptions, the stability and convergence are established by the energy argument, and the error is of order k2$$ {k}&#x0005E;2 $$, where k$$ k $$ is the parameter for the time grids. Numerical experiments validate the theoretical estimate. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations. [ABSTRACT FROM AUTHOR]

In this paper, we adopt the discontinuous Galerkin finite element method and the enriched Crouzeix‐Raviart finite element method to study the magnetohydrodynamic (MHD) Stokes eigenvalue problem describing the flow of a viscous and electrically conducting fluid in a duct under the influence of a uniform magnetic field. We give the convergence and error analysis for the approximations, and the theoretical analysis and numerical experiments show that the methods are effective and can be applied to general domains. We also explore the influence of the Hartmann number on the eigenpairs and the consequential variation of the eigenstructure with the magnetic field by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, a delayed mosquito population suppression model with stage and sex structure is constructed incorporating periodic releases of the sterile mosquito and its sexual lifespan. Sterile mosquitoes are released periodically into the field to suppress the wild mosquito population, and only sexually active sterile mosquitoes are included in the interaction system of these two populations. According to the relationship between the release period T$$ T $$ and the sexual lifespan T1$$ {T}_1 $$, we study the dynamic behaviors of the system, such as the existence of positive periodic solutions and the stability of extinction equilibrium in three cases. A series of numerical simulations are performed, which not only verify the reliability of the theoretical results but also make a numerical analysis of the open problems raised in the theoretical research. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a modified marker and cell (MMAC) method for solving the steady‐state Stokes equations with Dirichlet boundary condition. We reconstruct the marker and cell (MAC) schemes by using the quadratic Lagrange extrapolation method to approximate the value of ghost points near the boundary. First, we prove the stability of the proposed scheme rigorously. Then, we obtain the second‐order superconvergence for pressure in the discrete L2$$ {L}^2 $$ norm and velocity in the discrete H1$$ {H}^1 $$ norm by constructing auxiliary functions and discretizing parameters. Meanwhile, we present two MMAC schemes for the time‐dependent Stokes equations by a similar method. Finally, we provide some numerical experiments to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]

We analyze a mathematical model of a tumor that includes the interactions among tumor cells (live or dead), macrophages, endothelial cells, and the cytokines based on a system of partial differential equations which describes inhibition of tumor growth by granulocyte‐macrophage colony‐stimulating factor (GM‐CSF) treatment. The aim of the model is to predict the growth of the tumor volume under partial blocking of hypoxia‐inducible factor (HIF)‐1 or stabilization of HIF‐2, with injection of GM‐CSF. It was assumed that tumor is a spherical and the treatment by GM‐CSF is not optimized. In this paper, we do not assume that tumor is a spherical model and we develop a dual dynamic programming approach to formulate a verification condition of an approximate treatment for an injection of GM‐CSF. Next, we analyze numerically an ε$$ \varepsilon $$‐optimal treatment. [ABSTRACT FROM AUTHOR]

Since the pioneering work of Turing, it has been known that diffusion can destablise a homogeneous solution that is stable in the underlying model in the absence of diffusion. The destabilisation of the homogeneous solutions leads to the generation of patterns. In recent years, techniques have been developed to analyse so‐called localised spatial structures. These are solutions in which the spatial structure occurs in a localised region. Unlike Turing patterns, they do not spread out across the whole domain. We investigate the existence of localised structures that occur in two predator‐prey models. The functionalities chosen have been widely used in the literature. The existence of localised spatial structures has not investigated previously. Indeed, it is easy to show that these models cannot exhibit the Turing instability. This has perhaps led earlier researchers to conclude that interesting spatial solutions can therefore not occur for these models. The novelty of our paper is that we show the existence of stationary localised patterns in systems which do not undergo the Turing instability. The mathematical tools used are a combination of Linear and weakly nonlinear analysis with supporting numerical methods. By combining these methods, we are able to identify conditions for a wide range of increasing exotic behaviour. This includes the Belyckov‐Devaney transition, a codimension two spatial instability point and the formation of localised patterns. The combination of spectral computations and numerical simulations reveals the crucial role played by the Hopf bifurcation in mediating the stability of localised spatial solutions. Finally, numerical solutions in two spatial dimensions confirms the onset of intricate spatio‐temporal patterns within the parameter regions identified within one spatial dimension. [ABSTRACT FROM AUTHOR]

This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain Ω⊂ℝ2$$ \Omega \subset {\mathrm{\mathbb{R}}}&amp;#x0005E;2 $$. Here, the temporal partial derivative is in the sense of Caputo with order α∈(0,1)$$ \alpha \in \left(0,1\right) $$, and the spatial partial derivatives are of Riesz type with orders β,γ∈(0,1)$$ \beta, \gamma \in \left(0,1\right) $$ in x$$ x $$‐ and y$$ y $$‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

A second‐order accurate, linear numerical method is analyzed for the Landau–Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non‐convexity constraint of unit length of the magnetization. The numerical method is based on the second‐order backward differentiation formula in time, combined with an implicit treatment for the linear diffusion term from the harmonic mapping part and explicit extrapolation for the nonlinear terms. Afterward, a projection step is applied to normalize the numerical solution at a point‐wise level. This numerical scheme has shown extensive advantages in the practical computations for the physical model with large damping parameters, which comes from the fact that only a linear system with constant coefficients (independent of both time and the updated magnetization) needs to be solved at each time step, and has greatly improved the numerical efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme has not been available. In this paper, we provide a rigorous error estimate of the numerical scheme, in the discrete ℓ∞(0,T;ℓ2)∩ℓ2(0,T;Hh1)$$ {\ell}&amp;#x0005E;{\infty}\left(0,T;{\ell}&amp;#x0005E;2\right)\cap {\ell}&amp;#x0005E;2\left(0,T;{H}_h&amp;#x0005E;1\right) $$ norm, under suitable regularity assumptions and reasonable ratio between the time step size and the spatial mesh size. In particular, the projection operation is nonlinear, and a stability estimate for the projection step turns out to be highly challenging. Such a stability estimate is derived in details, which will play an essential role in the convergence analysis for the numerical scheme, if the damping parameter is greater than 3. [ABSTRACT FROM AUTHOR]

Bratu‐type equation has wide applications in physics, finance, and other fields. Also, fractional analysis has been a popular topic recently. It is difficult to find the analytical solution once we add the fractional operator on the left side of the equation. In this work, we apply explicit and implicit finite difference methods to solve the fractional Bratu equation. From the numerical examples, we will see that the explicit solution is not accurate, and the implicit solution based on Newton's method is efficient in some sense. Some theoretical results are mentioned in the paper. [ABSTRACT FROM AUTHOR]

The linear elasticity problem has important applications in structural analysis and engineering design. It is shown that the classical Crouzeix–Raviart finite element method is unstable to solve the linear elasticity eigenvalue problem with the pure traction boundary condition. In this paper, first we propose a new scheme with the stabilization terms. Then we prove the a priori error estimates for approximate eigenpairs. Finally, we carry out numerical experiments using the stabilized scheme. Theoretical analysis and numerical results show that this scheme is locking free and efficient. [ABSTRACT FROM AUTHOR]

Improvements in technology for the production of microbial biomass from natural gas, which have been gaining importance in recent years, require the development and optimization of energy‐efficient bioreactor designs. The most advanced methods for developing and scaling up industrial biotechnological processes rely on detailed hydrodynamic modeling, in addition to classical approaches, as the main tool for analysis and large‐scale transfer of experimental information. This paper presents the results of a simulation of flows in a bioreactor circuit using the latest mathematical methods and numerical flow analysis tools for two‐phase bubble flows based on experimental data. [ABSTRACT FROM AUTHOR]

In this paper, we study the finite difference/iterative method for the fractional telegraph equation with Hadamard derivatives. The model is first transformed into an equivalent fractional integro‐differential equation, then the technic of exponential type meshes is adopted. The resulting discrete coefficients of Hadamard fractional integral own several graceful properties, which are crucial in numerical analysis. To conquer the difficulty caused by weak regularity, we also propose iterative schemes. The error estimate is equal to O(logt)n+γ,1

Previously, existence and uniqueness of a class of monotone similarity solutions for a nonlinear differential equation arising in magnetohydrodynamic Falkner-Skan flow were considered in the case of accelerating flows. It was shown that a solution satisfying certain monotonicity properties exists and is unique for the case of accelerated flows and some decelerated flows. In this paper, we show that solutions to the problem can exist for decelerated flows even when the monotonicity conditions do not hold. In particular, these types of solutions have nonmonotone second derivatives and are, hence, a distinct type of solution from those studied previously. By virtue of this result, the present paper demonstrates the existence of an important type of solution for decelerated flows. Importantly, we show that multiple solutions can exist for the case of strongly decelerated flows, and this occurs because of the fact that the solutions do not satisfy the aforementioned monotonicity requirements. [ABSTRACT FROM AUTHOR]

We study in this paper the well‐posedness and stability of three structures with interfacial slip and two infinite memories effective on the transverse displacement and the rotation angle. We consider a large class of kernels and prove that the system has a unique solution satisfying some regularity properties. Moreover, without restrictions on the values of the parameters, we show that the solution goes to zero at infinity and give an information on its speed of convergence in terms of the growth of kernels at infinity. A numerical analysis of the obtained theoretical results will be also given. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model that analyzes cancer treatment via radiotherapy and proposes ways to control its progression. To identify preventive measures for cancer in its early stages, scientists have studied both risk factors and protective factors. In our model, we consider the disease‐free equilibrium points, namely, the trivial equilibrium (TE), healthy cell absenteeism equilibrium (HCAE), cancer cell absenteeism equilibrium (CCAE), and cancer cell incidence equilibrium (CCIE). We use nonlinear analysis techniques and the spectral radius method to study the stability and instability of systems. Since the reproduction number plays a critical role in stability analysis, we use the spectral radius method to evaluate it. We have also added a control function to the model to enhance it by including interactions between healthy and cancer cells. Optimization techniques are used to identify the limitations and needs of the problem and derive the best solutions to control the tumor. We conduct sensitivity analysis with respect to various parameters to study the model's robustness. To validate our methods and results, we provide simulations and numerical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we establish finite-region stability (FRS) and finite-region boundedness analysis methods to investigate the transient behavior of discrete two-dimensional Roesser models. First, by building special recursive formulas, a sufficient FRS condition is built via solvable linear matrix inequalities constraints. Next, by designing state feedback controllers, the finite-region stabilization issue is analyzed for the corresponding two-dimensional closed-loop system. Similar to FRS analysis, the finite-region boundedness problem is addressed for Roesser models with exogenous disturbances and corresponding criteria, and linear matrix inequalities conditions are reported. To conclude the paper, we provide numerical examples to confirm the validity of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the solutions, stability character, and asymptotic behavior of the difference equation [ABSTRACT FROM AUTHOR]

This paper discusses some basic dynamical properties of the chaotic finance system with parameter switching perturbation, and investigates chaos projective synchronization of the chaotic finance system with the time-varying delayed feedback controller, which are not fully considered in the existing research. Different from the previous methods, in this paper, the delayed feedback controller is not only time-varying, but also the time-varying delay is adaptive. Finally, an illustrate example is provided to show the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, new energy functionals are described via the variational approach method. By doing this, a new class of elastic curves is described in the three‐dimensional ordinary space. An alternative method is also investigated to compute critical points of the bending energy functionals acting on a class of magnetic curves. Then, classifications of these critical curves are presented as elastic magnetic curves of the Frenet–Serret vectors family. Moreover, the dynamics of the elastic magnetic curves of ferromagnetic and superparamagnetic models are discussed with their numerical and analytical analysis. [ABSTRACT FROM AUTHOR]

Threshold noise reduction methods of vibration signals have been widely researched and used. However, these methods are less efficient in such situation, including requiring a time-consuming and subjective to manual editing because different degree of noise signal requires selecting different characterization for filtering. In this paper, an efficient denoising method based on PDE for mechanical vibration signals time-frequency distribution is investigated, in which, a one-dimensional vibration signal is transformed into 2D time-frequency domain by using Gabor transform. This enables (i) simultaneously utilize both time and frequency characteristic for effectively multiple dimension signal denosing and (ii) isotropic and anisotropic characteristics to be imposed by employing PDE, which explicitly fit with the local structure of time-frequency signal. This paper analyzes the basic methods of isotropic and anisotropic diffusion filtering, investigates the anisotropic diffusion method based on local feature structure of 2D information, and conducts a set of comparative tests. Experiments show that this proposed method has a better performance of denoising than that of thresholding. At the same time, it is more handy than that of other methods, such as independent component analysis. Finally, problems and ways of improving the PDE-based filter method are analyzed in this paper. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an infinite integral concerning numerical computation in crystallography is investigated, which was studied in two recent articles, and integration by parts is employed for calculating this typical integral. A variable transformation and a single integration by parts lead to a new formula for this integral, and at this time, it becomes a completely definite integral. Using integration by parts iteratively, the singularity at the points near three points a D 0, 1, 2 can be eliminated in terms containing obtained integrals, and the factors of amplifying round-off error are released into two simple fractions independent of the integral. Series expansions for this integral are obtained, and estimations of its remainders are given, which show that accuracy 2-n is achieved in about 2n operations for every value in a given domain. Finally, numerical results are given to verify error analysis, which coincide well with the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the blow-up phenomena for a class of fourth-order nonlinear wave equations with a viscous damping term utt - α uxxt + uxxxx = f(ux)x, x ∈ Ω, t > 0 with Ω = (0, 1) and α > 0. Here, f(s) is a given nonlinear smooth function. For 0 < α < p - 1, we prove that the blow-up occurs in finite time for arbitrary positive initial energy and suitable initial data. This result extends the recent results obtained by Xu et al. [ABSTRACT FROM AUTHOR]

A new defect-correction method based on the pressure projection for the stationary Navier-Stokes equations is proposed in this paper. A local stabilized technique based on the pressure projection is used in both defect step and correction step. The stability and convergence of this new method is analyzed detailedly. Finally, numerical examples confirm our theory analysis and validate high efficiency and good stability of this new method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Galerkin finite element method for the Cahn‐Hilliard‐Cook equation involving the Caputo‐type fractional derivative, which can be used to describe the interface phenomena for modeling the phase transitions with the random effects and the properties of shape memory. The regularity properties of mild solution to the given problem are presented, and a result concerning the convergence error estimate of the corresponding semidiscrete scheme is established. Finally, we construct the fully discrete scheme based on the approximations of the Mittag‐Leffler function, and the strong convergence error estimate of the proposed scheme is also studied. [ABSTRACT FROM AUTHOR]

In this work successive differentiation method is applied to solve highly nonlinear partial differential equations (PDEs) such as Benjamin-Bona-Mahony equation, Burger's equation, Fornberg-Whitham equation, and Gardner equation. To show the efficacy of this new technique, figures have been incorporated to compare exact solution and results of this method. Wave variable is used to convert the highly nonlinear PDE into ordinary differential equation with order reduction. Then successive differentiation method is utilized to obtain the numerical solution of considered PDEs in this paper. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method for computing numerical solutions of two-dimensional Stratonovich Volterra integral equations using one-dimensional modification of hat functions and two-dimensional modification of hat functions. The problem is transformed to a linear system of algebraic equations using the operational matrix associated with one-dimensional modification of hat functions and two-dimensional modification of hat functions. The error analysis of the method is given. The method is computationally attractive, and applications are demonstrated by a numerical example. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka-Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays on time scales, a permanence result for the model is obtained. Furthermore, based on the permanence result, by studying the Lyapunov stability theory of impulsive dynamic equations on time scales, we establish the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results, and our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new even if for both the case of the time scale [ABSTRACT FROM AUTHOR]

Heat transfer of a power-law non-Newtonian incompressible fluid in channels with porous walls has not been carefully studied using a proper numerical method despite a few constructions of approximate analytic solutions through the similarity transformation and perturbation method for Newtonian fluids (i.e. power-law index being one). In this paper, we propose a finite element method for the thermal incompressible flow equations. The incompressible condition is treated by a penalty formulation. Numerical solutions are validated by comparing them with an approximate analytic solution of the Navier-Stokes equation in the Newtonian fluid case. Then, the method is used to simulate the heat transfer of various power-law fluids. Additionally, unlike previous studies, we allow the thermal diffusivity to be a function of temperature gradient. The effect of different values of the parameters on the temperature and velocity is also discussed in this paper. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Anomalous diffusion problems are used to describe the evolution of particle's motion in crowded environments with many applications, such as modeling the intracellular transport and disordered media. In the present paper, we develop a Petrov–Galerkin spectral method for the fourth‐order anomalous fractional diffusion equations. For the dimension reduction, we use a discretization in time by the convolution quadrature. We then introduce the basis sets for the trial‐and‐test spaces using modal Bernstein basis functions with a presentation of the method in a weak spectral formulation along with a discussion of the structure of the resulting systems, the convergence, and stability of the proposed method. The theoretical results are supported by illustrating some numerical examples. [ABSTRACT FROM AUTHOR]

Every now and then, there has been natural or man‐made calamities. Such adversities instigate various institutions to find solutions for them. The current study attempts to explore the disaster caused by the micro enemy called coronavirus for the past few months and aims at finding the solution for the system of nonlinear ordinary differential equations to which q−homotopy analysis transform method (q−HATM) has been applied to arrive at effective results. In this paper, there are eight nonlinear ordinary differential equations considered and to solve them the advanced fractional operator Atangana‐Baleanu (AB) fractional derivative has been applied to produce better understanding. The outcomes have been presented in terms of plots. Ultimately, the present study assists in examining the real‐world models and aids in predicting their behavior corresponding to the parameters considered in the models. [ABSTRACT FROM AUTHOR]

In this paper, an efficient numerical procedure for the generalized nonlinear time‐fractional Klein–Gordon equation is presented. We make use of the typical finite difference schemes to approximate the Caputo time‐fractional derivative, while the spatial derivatives are discretized by means of the cubic trigonometric B‐splines. Stability and convergence analysis for the numerical scheme are discussed. We apply our scheme to some typical examples and compare the obtained results with the ones found by other numerical methods. The comparison shows that our scheme is quite accurate and can be applied successfully to a variety of problems of applied nature. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the study of an inverse problem that occurs during the pressing of rapeseeds, where some physical parameters influence on rapeseed oil extraction yield. Our objective is to identify the consolidation coefficient of the press cake, the inverse characteristic time of consolidation in press cake, and inside the rapeseed in order to increase the rapeseed oil extraction yield. Three questions will be addressed: the identifiability, the identification, and the stability of the inverse problem. Finally, we provide numerical results to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The article examines the possibilities of numerical solution of chimney load from the effect of wind. The shear‐stress transport (SST) k‐ω turbulence model in ANSYS Fluent software is used to evaluate the task of the flow around the circumference of the rough cylinder. Calculations are performed on two different meshes that lead to the solution using wall function and near wall modeling. These two solution approaches in terms of defining wall roughness are presented in the paper by evaluating of the time dependence of the mean pressure coefficient distribution at the circumference, drag coefficient, and lift coefficient. The accuracy of the calculations is verified with parameters determined according to valid standards. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of delay on the asymptotic behavior of Nicholson's blowflies model with patch structure and multiple time-varying delays. By using the fluctuation lemma and some differential inequality technique, delay-dependent criteria are obtained for the global attractivity of the addressed system. Meanwhile, some numerical examples are given to illustrate the feasibility of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, three conservative finite volume element schemes are proposed and compared for the modif ied Korteweg-de Vries equation, especially with regard to their accuracy and conservative properties. The schemes are constructed basing on the discrete variational derivative method and the finite volume element method to inherit the properties of the original equation. The theoretical analysis show that three schemes are conservative under suitable boundary conditions as well as unconditionally linear stability. Numerical experiments are given to confirm the theoretical results and the capacity of the proposed methods for capturing the solitary wave phenomena. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Hepatitis B virus (HBV) and its vaccination strategy may affect human immunodeficiency virus (HIV) transmission dynamics because both viruses have synergistic effects. To quantitatively assess the potential impact of HBV and its vaccination strategy on HIV transmission dynamics at the population level, in this paper, we formulate a deterministic compartmental model that describes the joint dynamics of HBV and HIV. We first derive the explicit expressions for the basic reproduction numbers of HIV and HBV and analyze the dynamics of HIV and HBV subsystems, respectively. Then a systematic qualitative analysis of the full system is also provided, which includes the local and global behavior. By using a set of reasonable parameter values, the full system is numerically investigated to assess the potential impact of HBV and its vaccination strategy on HIV transmission. The direct and indirect population level impact of HBV on HIV is demonstrated by calculating the fraction of HIV infections attributable to HBV and the difference between HIV prevalence in the presence and absence of HBV, respectively. The findings imply that the increase of HBV vaccination rate may unusually accelerate HIV epidemics indirectly, although the direct effect of HBV on HIV transmission decreases as HBV vaccination rate increases. Finally, the potential impact of HIV on HBV transmission dynamics is investigated by way of parenthesis. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the issue of stability of multi-group coupled systems on networks with multi-diffusion (MCSNMs) is mainly analyzed. Utilizing graph theory, a novel and practical method of constructing a proper Lyapunov function for the MCSNMs is presented. Furthermore, based on the graph-theoretic approach and the proposed Lyapunov function, sufficient criteria, in the term of Lyapunov function and coefficients of the system, respectively, are derived to ensure the stability of the MCSNMs. Apart from accessibility to checking, the proposed results can generalize the corresponding results published in a previous time. Finally, the effectiveness and feasibility of the obtained results are demonstrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a computational technique based on the pseudo-spectral method for the solution of distributed optimal control problem for the viscous Burgers equation. By using pseudo-spectral method, the problem is converted to a classical optimal control problem governed by a system of ordinary differential equations, which can be solved by well-developed direct or indirect methods. For solving the resulting optimal control problem, we present an indirect method by deriving and numerically solving the first-order optimality conditions. Numerical tests involving both unconstrained and constrained control problems are considered. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies a fractional‐order modelling chronic wasting disease (CWD). The basic results on existence, uniqueness, non‐negativity, and boundedness of the solutions are investigated for the considered model. The criterion for local as well as global stability of the equilibrium points is derived. A numerical analysis for Hopf‐type bifurcation is presented. Finally, numerical simulations are provided to justify the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we numerically analyse a phase‐lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one‐dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution. [ABSTRACT FROM AUTHOR]