An Iterative‎ ‎Method for‎ ‎Numerically‎ ‎Solving a Class of Linear Volterra Delay Integral Equations

Document Type : Original Scientific Paper

Authors

‎Department of Mathematics, ‎Shahed University, ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran

10.22052/mir.2025.256332.1502

Abstract

‎In this paper‎, ‎a numerical method based on a recursive relation (sequence) is presented for numerically solving a class of linear Volterra delay integral equations (VDIEs)‎, ‎where the recursive relation is obtained from the considered integral equation itself‎.
‎For this purpose‎, ‎first‎, ‎using the Banach fixed point theorem‎, ‎the existence and uniqueness of the solution to the considered VDIEs are proven‎.
‎It is also proven that the sequence mentioned above converges to the solution of the equation‎. ‎Then‎, ‎by considering a finite number of terms of the said sequence‎, ‎an approximation to the solution of the equation is obtained‎.
‎Finally‎, ‎some numerical examples are given to verify the accuracy and efficiency of the proposed method‎.

Keywords

Main Subjects


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