A High-Order Compact (HOC) Implicit Difference Scheme and a Multigrid Method for Solving 3D Unsteady Reaction Diffusion Equations

Lili Wu and Xiufang Feng
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Lili Wu: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
Xiufang Feng: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Mathematics, 2019, vol. 7, issue 12, 1-11

Abstract: A high-order compact (HOC) implicit difference scheme is proposed for solving three-dimensional (3D) unsteady reaction diffusion equations. To discretize the spatial second-order derivatives, the fourth-order compact difference operators are used, and the third- and fourth-order derivative terms, which appear in the truncation error term, are also discretized by the compact difference method. For the temporal discretization, the multistep backward Euler formula is used to obtain the fourth-order accuracy, which matches the spatial accuracy order. To accelerate the traditional relaxation methods, a multigrid method is employed, and the computational efficiency is greatly improved. Numerical experiments are carried out to validate the accuracy and efficiency of the present method.

Keywords: reaction diffusion equation; multigrid method; high-order compact scheme; implicit scheme; nonlinear reaction term (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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