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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]

Computer viruses present a substantial threat to our daily lives. Traditional models for the propagation of computer viruses primarily concentrate on network structures. In this paper, we take into account the constrained availability of resources in the context of computer virus prevention and control. We introduce a computer virus propagation model based on resource limitations. By examining the stability of both toxic and non-toxic equilibria within the model, we employ Matlab and Python for numerical analysis to simulate various computer virus propagation scenarios. Additionally, we present corresponding defense mechanisms for combatting these viruses. [ABSTRACT FROM AUTHOR]

We study the implementation of a Chebyshev spectral method with forward Euler integrator proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper. • Convergence of a spectral method for a peridynamic formulation of Richards' equation. • Existence and uniqueness of the solution by its stability and compactness properties. • Simulations to numerically verify the existence of the weak solution to the model. [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]

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]

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: In this paper, we analyze an SIS epidemic model with partially protective vaccination of efficacy e ∈[0, 1]. The model exhibits backward bifurcation for certain parameter values. The primary aim of this paper is to investigate the possibility of eliminating the infections in static as well as exponentially growing populations with a public health strategy based solely on vaccination. The critical vaccination rate ψ * above which the endemic infection dies out and the conditions on model parameters that ensure its existence are obtained. It has been found that eliminating the infection requires an application of control measures other than vaccination to reduce the basic reproduction number to below the reinfection threshold and then vaccinate susceptible individuals with a rate slightly greater than ψ *. The implication is that, generally, even if all newborns get vaccinated immediately after birth, an effective control is not necessarily assured except if the basic reproduction number is reduced to below the reinfection threshold. We further include the fatality of the infection and investigate its impact on the dynamics. Some numerical simulations are given to illustrate the theoretical analysis. [Copyright &y& Elsevier]

Abstract: In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier–Stokes equations. Second, it reports numerical simulation results for 1D shock tube problem, 2D impinging jet and 2D/3D broken dam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. [Copyright &y& Elsevier]

Abstract: Two families of tests for testing uniform association in cross-classification having ordered categories are considered. The test statistics of the tests in these two families are based on Burbea–Rao divergences between certain functions of the observed data. The objective of this paper is to compare these families. The comparison is done both theoretically and numerically. The theoretical study is based on asymptotic properties. For each family, two consistent approximations to the null distribution of the test statistic are studied: an estimation of the asymptotic null distribution and a bootstrap estimator. The power against fixed and local alternatives is also studied. Surprisingly, although the way in which each family measures deviations from the null hypothesis is rather different, the large sample power properties of these two families are quite similar, since both families are able to detect the same set of local alternatives. So, they should be compared for finite sample sizes. This task is numerically investigated through some simulation experiments. [Copyright &y& Elsevier]

Abstract: This paper presents a new numerical formulation for the simulation of immiscible and incompressible three-phase water–gas–oil flows in heterogeneous porous media. We take into account the gravitational effects, both variable permeability and porosity of porous medium, and explicit spatially varying capillary pressure, in the diffusive fluxes, and explicit spatially varying flux functions, in the hyperbolic operator. The new formulation is a sequential time marching fractional-step procedure based in a splitting technique to decouple the equations with mixed discretization techniques for each of the subproblems: convection, diffusion, and pressure–velocity. The system of nonlinear hyperbolic equations that models the convective transport of the fluid phases is approximated by a modified central scheme to take into account the explicit spatially discontinuous flux functions and the effects of spatially variable porosity. This scheme is coupled with a locally conservative mixed finite element formulation for solving parabolic and elliptic problems, associated respectively with the diffusive transport of fluid phases and the pressure–velocity problem. The time discretization of the parabolic problem is performed by means of an implicit backward Euler procedure. The hybrid-mixed formulation reported here is designed to handle discontinuous capillary pressures. The new method is used to numerically investigate the question of existence, and structurally stable, of three-phase flow solutions for immiscible displacements in heterogeneous porous media with gravitational effects. Our findings appear to be consistent with theoretical and experimental results available in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, the dynamics of an impulsively controlled predator–prey system with the Hassell–Varley functional response are studied. Under impulsive control, the conditions for the existence of a stable prey-free solution and for the permanence of the system are investigated by using Floquet theory and comparison theorems. Also the existence of a nontrivial periodic solution under some conditions is shown via the bifurcation theorem. Finally, numerical simulations are given to substantiate our theoretical results and to illustrate various dynamical behaviors of the system. [Copyright &y& Elsevier]

Abstract: This paper provides the impulsive control for chaotic systems based on Takagi–Sugeno (T–S) model. A less conservative impulsive control scheme for chaotic systems based on their T–S fuzzy model is presented. Then the proposed impulsive control scheme is successfully applied to stabilize Lorenz system and the numerical simulation illustrates the effectiveness of our results. [Copyright &y& Elsevier]

Abstract: System characteristics of a two-unit repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor for an operating unit failure is possibly considered. Time to failure and time to repair of the operating units are assumed to follow exponential distributions. In addition, the recovery time and reboot time of the failed units also follow exponential distributions. When time to failure, time to repair, recovery time and reboot time are with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, an impulsive control of bifurcations method is developed. Sufficient conditions for the asymptotical stability of an impulsive control system are derived. Comparison has been made between it and a typical feedback control method. Numerical simulations are cited to illustrate the methodology and to verify the theoretical results. [Copyright &y& Elsevier]

Abstract: In the simulation of dynamical systems exhibiting an ultraslow decay, differential equations of fractional order have been successfully proposed. In this paper we consider the problem of numerically solving fractional differential equations by means of a generalization of k-step Adams–Moulton multistep methods. Our investigation is focused on stability properties and we determine intervals for the fractional order for which methods are at least -stable. Moreover we prove the A-stable character of k-step methods for and . [Copyright &y& Elsevier]