An efficient high‐order algorithm for solving systems of reaction‐diffusion equations

Abstract

An efficient higher-order finite difference algorithm is presented in this article for solving systems of twodimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

Higher Order Compact Finite Difference Method for the Solution of 2-D Time Fractional Diffusion Equation

“…The error decreases when we decrease the size ℎ and value of . To evaluate the convergence order of our proposed method defined in [28], plugℎ = = 1 4 and halving the grid size. We see that the error is decreasing regularly, the results for ‖ ‖ 2 and the convergence rate are given in Table 1, Table 2 and Table 3.…”

Singly diagonally implicit runge-kutta method for time-dependent reaction-diffusion equation

“…In this article, we first apply the compact high-order approximation developed in [14] to turn the time-dependent reaction-diffusion equation given in Eq. (1) into a system of ordinary differential equations (ODE).…”

“…In [14], an efficient fourth-order algorithm based on Padé approximation was presented for solving the two-dimensional equation. It is fourth-order accurate in both the temporal and spatial dimensions, and requires only a compact stencil as used by the standard second-order CrankNicholson algorithm.…”

An implicit compact finite difference method for the fractional reaction-subdiffusion equation

“…Liao et al [7] implemented a CFD scheme for reaction-diffusion problems. A CFD scheme for the generalized one dimensional Sine-Gordon equation with error analysis was introduced in [4].…”