Computational method for Volterra integro-differential equations of the second kind

Authors

  • Abdullahi Muhammed Ayinde
    Department of Mathematics, University of Abuja, FCT, 900211, Nigeria
  • Adam Ajimoti Ishaq
    Department of Physical Sciences, Al-Hikmah University, Ilorin, Nigeria
  • Lukman Olalekan Ahmed
    Department of Mathematics, Baze University, Abuja, Nigeria
  • Emmanuel Jacob
    Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria

Keywords:

Volterra integro-differential equations, Interpolation technique, Stability analysis, Collocation technique

Abstract

This study presents a computational method (CM) for solving second-kind Volterra integro-differential equations (VIDEs), which are widely used in engineering, physics, biology, and control systems. The method combines interpolation and collocation techniques to produce a continuous one-step computational scheme that accurately approximates the solution while maintaining stability and convergence properties. Consistency, zero-stability, order of accuracy, convergence, and the region of absolute stability are examined to confirm the suitability of the method for both linear and nonlinear problems. Numerical experiments with selected VIDEs compare the CM with the fifth--order Adams–Bashforth–Moulton predictor--corrector method, the two-point three-step block method, the trigonometrically fitted block method, the Haar wavelet method, and trapezoidal schemes. Across the tested examples, the CM provides accurate, stable, and efficient approximations, making it a useful tool for solving complex integro-differential systems in practical applications.

Dimensions

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fig 1

Published

2026-07-15

How to Cite

Computational method for Volterra integro-differential equations of the second kind. (2026). African Scientific Reports, 5(2), 476. https://doi.org/10.46481/asr.2026.5.2.476

Issue

Volume 5, Issue 2, August 2026

Section

SPECIAL ISSUE IN HONOUR OF PROF. OLABODE MATTHIAS BAMIGBOLA
Copyright & Licensing

Copyright (c) 2026 Abdullahi Muhammed Ayinde, Adam Ajimoti Ishaq, Lukman Olalekan Ahmed, Emmanuel Jacob

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Computational method for Volterra integro-differential equations of the second kind. (2026). African Scientific Reports, 5(2), 476. https://doi.org/10.46481/asr.2026.5.2.476

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