SOLVING NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND WITH DISCONTINUOUS KERNELS BY USING THE OPERATIONAL MATRIX METHOD

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Аннотация

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.

Авторлар туралы

Simin Amirkhizi

Department of Mathematics, Tabriz Branch, Islamic Azad University

Email: stu.aghaei.s@iaut.ac.ir
Iran, Tabriz

Yaghoub Mahmoudi

Department of Mathematics, Tabriz Branch, Islamic Azad University

Email: mahmoudi@iaut.ac.ir
Iran, Tabriz

Ali Shamloo

Department of Mathematics, Shabestar Branch, Islamic Azad University

Хат алмасуға жауапты Автор.
Email: mahmoudi@iaut.ac.ir
Iran, Shabestar

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© Simin Aghaei Amirkhizi, Yaghoub Mahmoudi, Ali Salimi Shamloo, 2023