10.57647/ijm2c.2027.1701.03

A Hybrid Numerical Approach for Volterra Integro-Differential Equations via Block-Pulse and Muntz Functions

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  • Parvin Badihian,
  • Majid Tavassoli Kajani*1,
  1. Department of Mathematics, Isf.C., Islamic Azad University, Isfahan, Iran

Received: 14-02-2026

Revised: 16-05-2026

Accepted: 17-05-2006

Published in Issue 26-05-2026

Published Online: 18-05-2026

Copyright (c) 2025 Parvin Badihian, Majid Tavassoli Kajani (Author)

Creative Commons License

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

How to Cite

Badihian, P., & Tavassoli Kajani, M. (2026). A Hybrid Numerical Approach for Volterra Integro-Differential Equations via Block-Pulse and Muntz Functions. International Journal of Mathematical Modelling & Computations. https://doi.org/10.57647/ijm2c.2027.1701.03
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Abstract

In this paper, we present a novel set of hybrid functions using the Block-Pulse functions and a new class of Muntz functions to obtain numerical solutions for Volterra integro-differential equations (VIDEs). In this method, by implementing the collocation approach based on the new hybrid basis as the trial functions, the given VIDE is reformulated as a system of algebraic equations. As opposed to the existing methods that use M¨untz–Legendre polynomials, we utilize a new set of M¨untz functions that have distinct real roots in the interval [0, 1]. Furthermore, the convergence, stability and accuracy of the method are studied. Numerical examples are included to demonstrate the efficiency and high accuracy of the proposed approach.

Keywords

  • Muntz functions,
  • Block-Pulse functions,
  • Collocation method,
  • Volterra integro-differential equation,
  • Convergence,
  • Stability
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