带卷积核的新一类非线性二阶积分微分 Volterra 方程的存在性与数值解法

IF 0.4 Q4 MATHEMATICS, APPLIED Numerical Analysis and Applications Pub Date : 2024-09-13 DOI:10.1134/s1995423924030042

S. Lemita, M L. Guessoumi

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引用次数: 0

摘要

摘要本文研究了一类新的具有卷积核的非线性二阶整微分 Volterra 方程。我们利用 Schauder 定点定理推导出一些充分条件，以确定解的存在性和唯一性。此外，我们还应用 Nyström 方法求得了所提 Volterra 方程的近似解。我们还给出了一个数值示例来验证所得出的结果。

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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On Existence and Numerical Solution of a New Class of Nonlinear Second Degree Integro-Differential Volterra Equation with Convolution Kernel

Abstract

This paper considers a new class of nonlinear second degree integro-differential Volterra equation with a convolution kernel. We derive some sufficient conditions to establish the existence and uniqueness of solutions by using Schauder fixed point theorem. Moreover, the Nyström method is applied to obtain the approximate solution of the proposed Volterra equation. A numerical examples are given to validate the adduced results.

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.