Numerical solution for a generalized form of nonlinear cordial Volterra integral equations using quasilinearization and Legendre-collocation methods

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-09-12 DOI:10.1016/j.apnum.2024.09.013

引用次数: 0

Abstract

In this article, we propose a numerical method for a general form of nonlinear cordial Volterra integral equations. We discuss conditions that under them the problem has solutions. Since the existence of solutions for the problem depends on the solvability of a scalar equation and also a linear form of the problem, then we employ quasilinearization technique in which solving a nonlinear problem is reduced to solve a sequence of linear equations. The existence of solutions of linear equations and their quadratically convergence to the solutions of the nonlinear problem is considered. For the numerical solution of the produced linear equations we apply Legendre-collocation method along with a regularization technique for the quadrature formulas. We discuss the error analysis of the collocation method considering that the cordial Volterra integral operators are noncompact. To test the efficiency and accuracy of the proposed method, the solution of different cases of numerical examples are reported.

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用准线性化和 Legendre-collocation 方法数值求解非线性 cordial Volterra 积分方程的广义形式

在这篇文章中，我们提出了一种针对一般形式的非线性 cordial Volterra 积分方程的数值方法。我们讨论了在这些条件下问题有解的条件。由于问题解的存在取决于标量方程的可解性以及问题的线性形式，因此我们采用了准线性化技术，将非线性问题的求解简化为线性方程序列的求解。我们考虑了线性方程解的存在性及其对非线性问题解的二次收敛性。对于所产生线性方程的数值求解，我们采用了 Legendre-collocation 方法以及正则公式的正则化技术。考虑到 Volterra 积分算子的非紧凑性，我们讨论了配准法的误差分析。为了测试所提方法的效率和准确性，报告了不同情况下的数值示例求解。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.