Convergence Analysis of Multi-Step Collocation Method to First-Order Volterra Integro-Differential Equation with Non-Vanishing Delay

Authors

  • Ahmet Ali Eashel Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, Urmia, Iran
  • Saeed Pishbin Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, Urmia, Iran
  • Parviz Darania Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 165, Urmia, Iran

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5766

Keywords:

Volterra integro-differential equation, Delay integro-differential equation, Multi-step collocation methods, Convergence analysis

Abstract

Generally, solutions to functional equations involving non-vanishing delays tend to exhibit lower regularity compared to those of smooth functions. In this context, we examine a first-order Volterra integro-differential equation (VIDE) with a non-vanishing delay, delving into the characteristics of its solutions. To enhance the accuracy of traditional one-step collocation methods [1], we employ multi-step collocation techniques to obtain numerical solutions for the VIDE with non-vanishing delay. The global convergence properties of the multi-step numerical approach are scrutinized using the Peano Kernel Theorem. Subsequently, for comparative analysis, we utilize a one-step collocation method to numerically solve this equation, showcasing the effectiveness and precision of the multi-step collocation method.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Ahmet Ali Eashel, Saeed Pishbin, Parviz Darania

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How to Cite

Convergence Analysis of Multi-Step Collocation Method to First-Order Volterra Integro-Differential Equation with Non-Vanishing Delay. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5766. https://doi.org/10.29020/nybg.ejpam.v18i2.5766