{"title":"求解第二类 Volterra 积分方程系统的并行算法","authors":"V.O. Tykhokhod, V.A. Fedorchuk","doi":"10.15407/emodel.45.06.003","DOIUrl":null,"url":null,"abstract":"The problem of increasing the effectiveness of the study of integral models of dynamic systems is considered. A parallel algorithm for solving a system of Volterra linear integral equations of the second kind based on the quadrature method of numerical integration is proposed. The algo-rithm was implemented in the MATLAB computer mathematics system in the form of an m-function. The program uses the MATLAB Distributed Computing Toolbox infrastructure to manage workflows and distribute computations between them on multi-core processors. Com-putational experiments were conducted on a model example using the Symbolic Math Toolbox package for symbolic calculations and a comparison of the execution of parallel calculations with the execution time of the implementation of a sequential algorithm. The results showed a significant increase in the speed of research of integral models on multi-core processors when using the proposed algorithm and its computer implementation.","PeriodicalId":474184,"journal":{"name":"Èlektronnoe modelirovanie","volume":"690 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Parallel Algorithm for Solving Systems of Volterra Integral Equations of the Second Kind\",\"authors\":\"V.O. Tykhokhod, V.A. Fedorchuk\",\"doi\":\"10.15407/emodel.45.06.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of increasing the effectiveness of the study of integral models of dynamic systems is considered. A parallel algorithm for solving a system of Volterra linear integral equations of the second kind based on the quadrature method of numerical integration is proposed. The algo-rithm was implemented in the MATLAB computer mathematics system in the form of an m-function. The program uses the MATLAB Distributed Computing Toolbox infrastructure to manage workflows and distribute computations between them on multi-core processors. Com-putational experiments were conducted on a model example using the Symbolic Math Toolbox package for symbolic calculations and a comparison of the execution of parallel calculations with the execution time of the implementation of a sequential algorithm. The results showed a significant increase in the speed of research of integral models on multi-core processors when using the proposed algorithm and its computer implementation.\",\"PeriodicalId\":474184,\"journal\":{\"name\":\"Èlektronnoe modelirovanie\",\"volume\":\"690 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Èlektronnoe modelirovanie\",\"FirstCategoryId\":\"0\",\"ListUrlMain\":\"https://doi.org/10.15407/emodel.45.06.003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Èlektronnoe modelirovanie","FirstCategoryId":"0","ListUrlMain":"https://doi.org/10.15407/emodel.45.06.003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
研究考虑了提高动态系统积分模型研究效率的问题。在数值积分正交法的基础上，提出了一种求解 Volterra 第二类线性积分方程组的并行算法。该算法以 m 函数的形式在 MATLAB 计算机数学系统中实现。该程序使用 MATLAB 分布式计算工具箱基础设施来管理工作流，并在多核处理器上分配它们之间的计算。使用符号计算的符号数学工具箱软件包对一个模型示例进行了计算实验，并对并行计算的执行时间与顺序算法的执行时间进行了比较。结果表明，使用所提出的算法及其计算机实现，在多核处理器上研究积分模型的速度明显提高。
A Parallel Algorithm for Solving Systems of Volterra Integral Equations of the Second Kind
The problem of increasing the effectiveness of the study of integral models of dynamic systems is considered. A parallel algorithm for solving a system of Volterra linear integral equations of the second kind based on the quadrature method of numerical integration is proposed. The algo-rithm was implemented in the MATLAB computer mathematics system in the form of an m-function. The program uses the MATLAB Distributed Computing Toolbox infrastructure to manage workflows and distribute computations between them on multi-core processors. Com-putational experiments were conducted on a model example using the Symbolic Math Toolbox package for symbolic calculations and a comparison of the execution of parallel calculations with the execution time of the implementation of a sequential algorithm. The results showed a significant increase in the speed of research of integral models on multi-core processors when using the proposed algorithm and its computer implementation.
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