A Finite Difference Method for Smooth Solution of a System of Linear Volterra Integral Equations

Jalalvand, Mehdi; Mokhtarzadeh, Mohammad Reza; Toubaei, Sedigheh

doi:10.22055/jamm.2024.48011.2313

A Finite Difference Method for Smooth Solution of a System of Linear Volterra Integral Equations

Document Type : Original Paper

Authors

¹ Department of Mathematics, Shahid Chamran University of Ahvaz,

² School of Mathematics, Institute for Research in Fundamental Sciences,

³ Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

10.22055/jamm.2024.48011.2313

Abstract

In this paper, we propose a finite difference numerical method for the smooth solution of a system of linear Volterra integral equations. This method is a generalization of the finite difference method proposed in [11] and [12] for scalar linear Volterra integral equations. Error analysis of this method is presented via asymptotic expansion of the absolute error, and verification of accuracy is examined by two illustrative test problems.

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