The main purpose of the paper is to show how to use implicit–explicit Runge–Kutta methods
in a much more general context than usually found in the literature, obtaining very effective …

This paper demonstrates the use of higher order methods to solve some time-dependent stiff
PDEs. In the past, the most popular numerical methods for solving system of reaction …

In this paper, we propose an efficient numerical scheme for magnetohydrodynamics (MHD)
equations. This scheme is based on a second order backward difference formula for time …

Excerpt This book focuses on IMEX methods, with particular emphasis on their application to
systems of PDEs. IMEX methods have proven to be highly effective for solving a wide range …

This paper aims to developed a high-order and accurate method for the solution of one-
dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order …

We present and analyze an implicit--explicit timestep** procedure with finite element
spatial approximation for semilinear reaction--diffusion systems on evolving domains arising …

This paper presents a method by combining the semi-implicit spectral deferred correction
(SDC) method with the operator splitting scheme to simulate the fractional Gray-Scott (GS) …

Mathematical modeling of pattern formation in developmental biology leads to non-linear
reaction–diffusion systems which are usually highly stiff in both diffusion and reaction terms …

In this paper a numerical procedure is presented for solving a class of three-dimensional
Turing system. First, we discrete the spatial direction using element free Galerkin (EFG) …

Nonlinear reaction–diffusion systems are often employed in mathematical modeling for
pattern formation. Most of the work to date has been concerned within one-dimensional or …