An improved Bernoulli collocation method for solving Volterra integral equations

Authors

  • Anahita Khansari Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
  • Saeed Khezerloo Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
  • Mustafa Nouri Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
  • Muhammad Arghand Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

Keywords:

Bernoulli polynomials, shifted Chebyshev polynomials, Bernoulli collocation method (BCM), Improved Bernoulli collocation method (IBCM), Volterra integral equation s (VIEs)

Abstract

In this work, an improved collocation method based on the Bernoulli polynomials is presented to solve the Volterra integral equation (VIE) of the second kind. The main idea of the proposed method is to improve the results of the classic Bernoulli collocation method (BCM) by dividing the interval into some sub-intervals and
considering the collocation points on each of them. Here, the zeros of the shifted Chebyshev polynomials (SCPs) are considered as collocation points. Then, BCM is applied step by step from the first sub-interval to the last one. By this process, a system of algebraic equations is attained for each sub-interval that could be easily solved. Convergence of the scheme is analyzed. For the purpose of demonstrating the validity, applicability, and efficiency of the suggested scheme several numerical
examples are provided. Numerical results illustrate that the accuracy of the improved Bernoulli collocation method (IBCM) is more than BCM.

Published

2025-11-02

Issue

Vol. 19

Section

Vol. 19, No. 6, (2025)

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