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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2023 Volume 63, Number 11, Page 1849 (Mi zvmmf11649)

This article is cited in 1 paper

Ordinary differential equations

Solving nonlinear Volterra integral equations of the first kind with discontinuous kernels by using the operational matrix method

Simin Aghaei Amirkhizia, Yaghoub Mahmoudia, Ali Salimi Shamloob

a Department of Mathematics, Tabriz Branch, Islamic Azad University Tabriz, Iran
b Department of Mathematics, Shabestar Branch, Islamic Azad University Shabestar, Iran

Abstract: A numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of operational matrices for this kind of equation is a cost-efficient scheme. Shifted Legendre polynomials are applied for solving Volterra integral equations with discontinuous kernels by converting the equation to a system of nonlinear algebraic equations. The convergence analysis is given for the approximated solution and numerical examples are demonstrated to denote the precision of the proposed method.

Key words: nonlinear Volterra integral equation, piecewise continuous kernel, operational matrix, smooth function.

UDC: 519.64

Received: 01.02.2023
Revised: 23.06.2023
Accepted: 25.07.2023

Language: English

DOI: 10.31857/S0044466923110030


 English version:
Computational Mathematics and Mathematical Physics, 2023, 63:11, 2069–2080

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© Steklov Math. Inst. of RAS, 2025