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.