求解非线性Fredholm积分方程的一种简单有效的格式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-27 DOI:10.3846/mma.2022.14194

A. Shahsavaran, F. Fotros

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引用次数: 1

摘要

本文构造了求第二类非线性Fredholm积分方程近似解的一种简单格式。为此，利用拉格朗日插值多项式和高斯-勒让德正交规则将源问题转化为非线性代数方程组。然后，用牛顿法求解得到的系统。其基本思想是选择拉格朗日插值点与高斯-勒让德积分点相同。这便于对方程的积分部分求值。我们证明了近似解一致收敛于精确解。并对近似解的稳定性进行了研究。该方法具有简单、快速、准确等优点，增强了其在实际应用中的适用性。最后，我们提供了一些测试示例。

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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An Effective and Simple Scheme for solving nonlinear Fredholm integral equations

In this paper, a simple scheme is constructed for finding approximate solution of the nonlinear Fredholm integral equation of the second kind. To this end, the Lagrange interpolation polynomials together with the Gauss-Legendre quadrature rule are used to transform the source problem to a system of nonlinear algebraic equations. Afterwards, the resulting system can be solved by the Newton method. The basic idea is to choose the Lagrange interpolation points to be the same as the points for the Gauss-Legendre integration. This facilitates the evaluation of the integral part of the equation. We prove that the approximate solution converges uniformly to the exact solution. Also, stability of the approximate solution is investigated. The advantages of the method are simplicity, fastness and accuracy which enhance its applicability in practical situations. Finally, we provide some test examples.

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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.