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Analysis on a Numerical Scheme with Second-Order Time Accuracy for Nonlinear Diffusion Equations

Analysis on a Numerical Scheme with Second-Order Time Accuracy for Nonlinear Diffusion Equations
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Year:    2021

Author:    Xia Cui, Guangwei Yuan, Fei Zhao

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 5 : pp. 777–800

Abstract

A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is studied. The scheme is constructed with two-layer coupled discretization (TLCD) at each time step. It does not stir numerical oscillation, while permits large time step length, and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinear schemes, the Crank-Nicolson (CN) scheme and the backward difference formula second-order (BDF2) scheme. By developing a new reasoning technique, we overcome the difficulties caused by the coupled nonlinear discrete diffusion operators at different time layers, and prove rigorously the TLCD scheme is uniquely solvable, unconditionally stable, and has second-order convergence in both space and time. Numerical tests verify the theoretical results, and illustrate its superiority over the CN and BDF2 schemes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2007-m2020-0058

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 5 : pp. 777–800

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Nonlinear diffusion problem Nonlinear two-layer coupled discrete scheme Second-order time accuracy Property analysis Unique existence Convergence.

Author Details

Xia Cui

Guangwei Yuan

Fei Zhao

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