带积分条件泊松方程的交替方向隐式解法

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2023-10-20 DOI:10.3846/mma.2023.18029

Olga Štikonienė, Mifodijus Sapagovas

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引用次数: 0

摘要

本文研究了具有非局部积分条件的二维椭圆型方程在矩形域近似的差分方程组的Peaceman-Rachford交替方向隐式方法的收敛性。本文的主要目的是分析具有非局部条件的差分特征值问题的谱结构。在特征向量完备的情况下，证明了迭代法的收敛性。将主要结果推广到差分方程组，近似于截断误差为0 (h4)的微分问题。

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ALTERNATING DIRECTION IMPLICIT METHOD FOR POISSON EQUATION WITH INTEGRAL CONDITIONS

In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4).

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来源期刊

Mathematical Modelling and Analysis 数学-数学

CiteScore

2.80

自引率

5.60%

发文量

审稿时长

4.5 months

期刊介绍： Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis.