A high-order compact difference method on fitted meshes for Neumann problems of time-fractional reaction–diffusion equations with variable coefficients

2021 ◽  
Vol 181 ◽  
pp. 598-623
Author(s):  
Yuan-Ming Wang
Keyword(s):  
Difference Method ◽  
Reaction Diffusion ◽  
Variable Coefficients ◽  
High Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Neumann Problems ◽  
Compact Difference ◽  
Compact Difference Method ◽  
Fractional Reaction

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

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1208 ◽  
Author(s):  
Lili Wu ◽  
Xiufang Feng
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Multigrid Method ◽  
Reaction Diffusion ◽  
High Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Implicit Difference Scheme ◽  
Euler Formula ◽  
Compact Difference

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.

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