On the computation of rational solutions of linear integro-differential equations with polynomial coefficients

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2023-07-20 DOI:10.1016/j.jsc.2023.102252

Moulay Barkatou, Thomas Cluzeau

引用次数: 0

Abstract

We develop the first algorithm for computing rational solutions of scalar integro-differential equations with polynomial coefficients. It starts by finding the possible poles of a rational solution. Then, bounding the order of each pole and solving an algebraic linear system, we compute the singular part of rational solutions at each possible pole. Finally, using partial fraction decomposition, the polynomial part of rational solutions is obtained by computing polynomial solutions of a non-homogeneous scalar integro-differential equation with a polynomial right-hand side. The paper is illustrated by examples where the computations are done with our Maple implementation.

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多项式系数线性积分-微分方程有理解的计算

我们提出了第一个计算多项式系数标量积分微分方程有理解的算法。它从寻找合理解决方案的可能极点开始。然后，界定每个极点的阶并求解代数线性系统，我们计算每个可能极点的有理解的奇异部分。最后，利用偏分式分解，通过计算一个具有多项式右手边的非齐次标量积分微分方程的多项式解，得到了有理解的多项式部分。本文通过使用Maple实现进行计算的示例进行了说明。

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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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.