基于一般线性方法求解Volterra积分方程的有效数值方法

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-05-06 DOI:10.1016/j.apnum.2025.04.011

Z. Ghahremani , A. Abdi , G. Hojjati

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引用次数: 0

摘要

本文给出了求解第二类Volterra积分方程的一组方法。该方法将一类特殊的常微分方程的一般线性方法与后向微分公式和格里高利求积分规则相结合。所提出的方法的顺序是根据基本的一般线性方法的内部阶段的数量和所提出的开始和结束方法的顺序推导出来的。数值实验证实了关于收敛阶和线性稳定性的理论结果，证明了所提方法在求解刚性方程方面的有效性。

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Efficient numerical methods based on general linear methods for Volterra integral equations

This paper presents a family of methods for solving Volterra integral equations of the second kind. The approach combines a special class of general linear methods for ordinary differential equations with the backward differentiation formulas and Gregory quadrature rules. The order of the proposed methods is derived in terms of the number of internal stages in the underlying general linear methods and the order of the proposed starting and finishing methods. Numerical experiments confirm the theoretical results regarding the convergence order and linear stability, demonstrating the efficiency of the proposed family of methods in solving stiff equations.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.