New Multi-step Collocation Methods for Non-standard Volterra Integral Equations

Authors

  • Hayder Abdullah Thabbah Department of Mathematics, Urmia University, Urmia, Iran
  • Parviz Darania Urmia University
  • Saeed Pishbin Department of Mathematics, Urmia University, Urmia, Iran

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6229

Keywords:

Non-standard integral equation, Error analysis, Multi-step collocation methods

Abstract

Non-standard Volterra integral equations (NVIEs) are in the category of non-linear Volterra integral
equations (VIEs) which appear in certain mathematical modelling processes.In the current study, new
multi-step collocation techniques have been employed to numerically address non-standard Volterra
integral equations. Several established outcomes concerning convergence of the numerical solution
for this problem are investigated. In conclusion, two test problems are thoroughly examined to
substantiate theoretical accomplishments in practical terms. Also, we apply one-step and multi-step
collocation methods to solve NVIEs and compare numerical results to show the efficiency and high
accuracy of the proposed method.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Hayder Abdullah Thabbah, Parviz Darania, Saeed Pishbin

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How to Cite

New Multi-step Collocation Methods for Non-standard Volterra Integral Equations. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6229. https://doi.org/10.29020/nybg.ejpam.v18i3.6229