The evolution of a dynamic system on complex curved 3D surfaces is essential for the understanding of natural phenomena, the development of new materials, and engineering design optimization. In this work, we study the viscous Cahn–Hilliard ...

In this paper, the space-time generalized finite difference scheme is applied to solve the nonlinear high-order Korteweg-de Vries equations in multiple dimensions. The proposed numerical scheme combines the space-time generalized finite ...

In this paper, we numerically investigate vector solitons with oscillatory phase backgrounds in the integrable coupled nonlinear Schrödinger equations, which are widely applied to varieties of physical contexts such as the simultaneous ...

In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous ...

In this current paper, we consider the problem of estimating the stress–strength parameter ψ = P ( X < Y ). This is done by using Bayesian and non-Bayesian approaches when X and Y are independent random variables from two exponential-Rayleigh ...

We present some efficient algorithms based on an exponential time differencing spectral deferred correction (ETDSDC) method for multidimensional second and fourth-order parabolic problems with non-periodic boundary conditions including Dirichlet, ...

This study focuses on unraveling key factors influencing predator–prey interactions with Crowley–Martin functional response. Specifically, it explores the roles of additional food sources, harvesting practices, hunting cooperation, fear and its ...

Analyzing uniform convergence of finite element method for a 2-D singularly perturbed convection–diffusion problem with exponential layers on Bakhvalov-type mesh remains a complex, unsolved problem. Previous attempts to address this issue have ...

We construct and analyse nonstandard finite difference (NSFD) schemes for two epidemic optimal control problems. Firstly, we consider the well-known MSEIR system that can be used to model childhood diseases such as the measles, with the ...

The aim of this work is to conduct a rigorous mathematical analysis for global dynamics and numerical simulation of a recognized viral marketing (VM) model, which is described by a system of ordinary differential equations (ODEs). We first ...

In this work, we propose a multidimensional continuum model for plasmid dissemination in biofilms via horizontal gene transfer. The model is formulated as a system of nonlocal partial differential equations derived from mass conservation laws and ...

Numerical techniques are widely used to simulate population dynamics in space. In vegetation dynamics, these techniques are very useful to investigate how plants grow, compete for resources, and react to environmental factors within the ...

In this paper, we have proposed and analyzed a predator–prey system introducing the cost of predation fear into the prey reproduction with Holling type-II functional response in the stochastic environment with the consideration of non-linear ...

This article establishes a bifurcation analysis of a singularly perturbed piecewise-smooth continuous predator–prey system with a sufficiently small parameter. The bifurcation that can generate limit cycles here is our main concern. To achieve ...

Within the context of a two-dimensional framework encompassing interacting species, an examination is conducted in this study on the double Allee effect and prey refuge, considering both species in the interaction. The stability of the feasible ...

This research focuses on devising a new fast difference scheme to simulate the Caputo tempered fractional derivative (TFD). We introduce a fast tempered λ F £ 2 − 1 σ difference method featuring second-order precision for a tempered time ...

• Fast tempered high order algorithm for Caputo tempered fractional derivative is proposed.
• Compact difference scheme with O ( h 4 ) for the fast algorithm is presented.
• Analyzing the tempered fractional Burgers equation in sound ...

In this work, we proposed a nonlinear mathematical model with fractional-order differential equations employed to illustrate the impacts of depleted forestry resources with the effect of toxin activity and human-caused fire. The numerical and ...

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical ...

The memristive chaotic systems have attracted much attention and have been thoroughly discussed. The analysis shows that the fractional-order system is closer to the real system, and the time-delay chaotic systems are of an infinite-dimension ...

Identification of the various dynamical kinetics relating to prey–predator interconnection is the main goal of theoretical ecologists. In addition to direct killing (the lethal effect) in prey–predator interactions, a number of studies have ...