In this paper, an effective numerical technique based on Lucas and Fibonacci polynomials
coupled with finite differences is developed for the solution of nonlinear reaction–diffusion …

The main focus of this article is to capture the patterns of reaction–diffusion Brusselator
model arising in chemical processes such as enzymatic reaction, formation of turing patterns …

An influence of random disturbances on the pattern formation in reaction–diffusion systems
is studied. As a basic model, we consider the distributed Brusselator with one spatial …

In this article, the authors approximate solution to the Brusselator model by Galerkin finite
element method and present a priori error estimate for the approximation. Further, we study …

We considered a mathematical model of the spread of the HIV-AIDS (Human
Immunodeficiency Virus-Acquired Immunodeficiency Syndromedisease). The model is of the …

We study a stochastic spatially extended population model with diffusion, where we find the
coexistence of multiple non-homogeneous spatial structures in the areas of Turing …

This paper mainly seeks to contribute to the study of a quasilinear parabolic reaction–
diffusion system of arbitrary order with initial conditions. Using potential analysis techniques …

In recent years, various numerical methods, including finite difference method (FDM), finite
volume method (FVM), and finite element method (FEM), have been devised to solve time …

This article presents an effective and simple approximation scheme to analytically
approximate solution behavior of a multi‐dimensional reaction–diffusion Brusselator system …

The problem with the analysis of noise-induced transitions between patterns in distributed
stochastic systems is considered. As a key model, we use the spatially extended dynamical …