{"title":"On the computation of rational solutions of linear integro-differential equations with polynomial coefficients","authors":"Moulay Barkatou, Thomas Cluzeau","doi":"10.1016/j.jsc.2023.102252","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>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 </span>partial fraction decomposition<span>, 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 </span></span><span>Maple</span> implementation.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"121 ","pages":"Article 102252"},"PeriodicalIF":1.1000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symbolic Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0747717123000664","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/7/20 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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.
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.
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