二阶Fredholm积分微分方程线性有理有限差分解SOR迭代法的改进

IF 0.5 Q3 MATHEMATICS

Malaysian Journal of Mathematical Sciences Pub Date : 2022-01-31 DOI:10.47836/mjms.16.1.09

M. M. Xu, J. Sulaiman, L. H. Ali

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引用次数: 0

摘要

本文的主要目的是发展基于三点线性有理有限差分正交离散格式的连续过松弛(RSOR)方法的改进，用于求解二阶线性Fredholm积分-微分方程(FIDE)的数值解。此外，为了说明该方法的优越性，给出了一些数值算例，并通过实现高斯-塞德尔(GS)、逐次过松弛(SOR)和RSOR三种方法进行了求解。最后，通过对结果的比较，验证了RSOR方法比其他两种方法更有效，特别是在考虑迭代次数和运行时间方面。

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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Refinement of SOR Iterative Method for the Linear Rational Finite Difference Solution of Second-Order Fredholm Integro-Differential Equations

The primary objective of this paper is to develop the Refinement of Successive Over-Relaxation (RSOR) method based on a three-point linear rational finite difference-quadrature discretization scheme for the numerical solution of second-order linear Fredholm integro-differential equation (FIDE). Besides, to illuminate the superior performance of the proposed method, some numerical examples are presented and solved by implementing three approaches which are the Gauss-Seidel (GS), the Successive Over-Relaxation (SOR) and the RSOR methods. Lastly, through the comparison of the results, it is verified that the RSOR method is more effective than the other two methods, especially when considering the aspects of the number of iterations and running time.

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来源期刊

Malaysian Journal of Mathematical Sciences MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.