第一类非线性Volterra积分方程的数值解

IF 0.4 Q4 MATHEMATICS Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-28 DOI:10.5269/bspm.63205
Boutheina Tair, M. Ghiat, Hmaza Guebbai, Mohamed Zine Aissaoui
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引用次数: 0

摘要

本文主要研究一类非线性Volterra方程的数值解。在一个必要条件下,我们给出了精确解的存在唯一性。本文提出了一种基于线性化和离散化两个基本部分的数值方法。我们从使用Nystrom方法的概念对方程进行离散化开始,对于线性化,我们使用牛顿方法。我们给出了证明该方法收敛性的定理。最后通过数值算例说明了该方法的有效性。
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Numerical solution of non-linear Volterra integral equation of the first kind
In this paper, we focus on the numerical solution of a nonlinear Volterra equation of the first kind. The existence and uniqueness of the exact solution is ensured under a necessary condition which we present next. We develop a numerical method based on two essential parts which are linearization and discretization. We start with the discretization of the equations using the concept of Nystrom's method and for the linearization we apply Newton's method. We present theorems that show the convergence of the proposed method. At the end, numerical  examples are presented to show the eficiency of our method.
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
140
审稿时长
25 weeks
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