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 …

A local meshless collocation method has been designed for solving reaction–diffusion
systems on surfaces. The proposed numerical procedure is based on Pascal polynomial …

Purpose The purpose of this study is to use the method of lines to solve the two-dimensional
nonlinear advection–diffusion–reaction equation with variable coefficients …

Purpose The purpose of this paper is to describe a novel universal error estimator and the
adaptive time-stepping process in the generalized single-step single-solve (GS4-1) …

Purpose This study aims to propose a new numerical method for solving non-linear partial
differential equations on irregular domains. Design/methodology/approach The main aim of …

In this study, we develop a nine-point compact difference scheme in exponential form to
solve two-dimensional second-order quasi-linear parabolic equations with Dirichlet …

The current paper proposes an efficient numerical procedure for solving the two-
dimensional Brusselator reaction–diffusion system. First, the time derivative is discretized by …

This paper presents the nonsymmetric interior penalty Galerkin (NIPG) finite element method
for a class of one-dimensional convection dominated diffusion problems with discontinuous …

This paper proposes the Boundary Knot Method with ghost points (BKM-G), which enhances
the performance of the BKM for solving 2D (3D) high-order Helmholtz-type partial differential …

This article presents a simple and reliable kernel-based meshless approximation scheme to
analyze the behavior of a two-dimensional coupled reaction–diffusion system. Combining …