Numerical Simulation of Initial Value Problem of Integro-differential Equation Models

IF 17.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-31 DOI:10.29020/nybg.ejpam.v17i1.5024

Faizah Alharbi, Sharifah Althubiti

引用次数: 0

Abstract

In this article, the Volterra-Fredholm integral equation (V-FIE) is derived from an initial value problem of kind integro-differential equation (IVP). We discuss the existence and uniqueness of the solution to the problem in Hilbert space. A numerical method is used to reduce this type of equation to System of Fredholm integral equations of the second kind(SFIEs). In light of this, the clustering method and the Galerkin method to solve the system of second-order Fredholm integral equations(SFIEs) and calculate the error in each case. Finally, the approximate and exact solutions are plotted on the same coordinate plane Using MATLAB code (2022).

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积分微分方程模型初值问题的数值模拟

在本文中，Volterra-Fredholm 积分方程（V-FIE）是从一种积分微分方程（IVP）的初值问题推导出来的。我们讨论了该问题在希尔伯特空间的解的存在性和唯一性。我们使用数值方法将这类方程简化为第二类弗雷德霍姆积分方程系统（SFIEs）。有鉴于此，采用聚类法和 Galerkin 法求解二阶弗雷德霍姆积分方程（SFIEs）系统，并计算每种情况下的误差。最后，使用 MATLAB 代码（2022）在同一坐标平面上绘制近似解和精确解。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.