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Open AccessArticle

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

by Lili Wu 1,2 and Xiufang Feng 1,*
1
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2
School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1208; https://doi.org/10.3390/math7121208
Received: 7 November 2019 / Revised: 4 December 2019 / Accepted: 5 December 2019 / Published: 9 December 2019
(This article belongs to the Section Mathematics and Computer Science)
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. View Full-Text
Keywords: reaction diffusion equation; multigrid method; high-order compact scheme; implicit scheme; nonlinear reaction term reaction diffusion equation; multigrid method; high-order compact scheme; implicit scheme; nonlinear reaction term
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Wu, L.; Feng, X. A High-Order Compact (HOC) Implicit Difference Scheme and a Multigrid Method for Solving 3D Unsteady Reaction Diffusion Equations. Mathematics 2019, 7, 1208.

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