Error Estimate and Superconvergence of a High-Accuracy Difference Scheme for Solving Parabolic Equations with an Integral Two-Space-Variables Condition
Year: 2018
Author: Liping Zhou, Shi Shu, Haiyuan Yu
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 362–389
Abstract
The initial-boundary value problems for parabolic equations with nonlocal conditions have been widely applied in various fields. In this work, we firstly build an implicit Euler scheme for an initial-boundary value problem of one dimensional parabolic equations with an integral two-space-variables condition. Then we prove that this scheme can reach the asymptotic optimal error estimate in the maximum norm. Next, the formulas used to approximate the solution derivatives with respect to time and spatial variables are presented, and it is proved for the first time that they have superconvergence. In the end, numerical experiments demonstrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0067
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 362–389
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Parabolic equation integral condition finite difference scheme asymptotic optimal error estimate superconvergence.
Author Details
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Error estimate and superconvergence of a high-accuracy difference scheme for 2D heat equation with nonlocal boundary conditions
Zhou, Liping
Yan, Yumei
Liu, Ying
AIMS Mathematics, Vol. 9 (2024), Iss. 10 P.27848
https://doi.org/10.3934/math.20241352 [Citations: 0]