非局部条件下非线性抛物型方程差分格式最大范数的稳定性

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2023-02-22 DOI:10.15388/namc.2023.28.31562

M. Sapagovas, Jurij Novickij

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引用次数: 0

摘要

构造并分析了一类具有非局部边界条件的非线性一维抛物方程的后向欧拉方法。本文的主要目的是研究差分格式在最大范数下的稳定性和收敛性。为此，我们使用m -矩阵理论。本文描述了一种新的解的误差估计方法，并构造了它的主体。最后给出了一些结论和讨论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On stability in the maximum norm of difference scheme for nonlinear parabolic equation with nonlocal condition

We construct and analyze the backward Euler method for one nonlinear one-dimensional parabolic equation with nonlocal boundary condition. The main objective of this article is to investigate the stability and convergence of the difference scheme in the maximum norm. For this purpose, we use the M-matrices theory. We describe some new approach for the estimation of the error of solution and construct the majorant for it. Some conclusions and discussion of our approach are presented.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.