Version 1
: Received: 23 May 2024 / Approved: 24 May 2024 / Online: 24 May 2024 (08:38:41 CEST)
How to cite:
Khansari, A.; Khezerloo, S.; Nouri, M.; Arghand, M. An Improved Bernoulli Collocation Method for Solving Volterra Integral Equations. Preprints2024, 2024051602. https://doi.org/10.20944/preprints202405.1602.v1
Khansari, A.; Khezerloo, S.; Nouri, M.; Arghand, M. An Improved Bernoulli Collocation Method for Solving Volterra Integral Equations. Preprints 2024, 2024051602. https://doi.org/10.20944/preprints202405.1602.v1
Khansari, A.; Khezerloo, S.; Nouri, M.; Arghand, M. An Improved Bernoulli Collocation Method for Solving Volterra Integral Equations. Preprints2024, 2024051602. https://doi.org/10.20944/preprints202405.1602.v1
APA Style
Khansari, A., Khezerloo, S., Nouri, M., & Arghand, M. (2024). An Improved Bernoulli Collocation Method for Solving Volterra Integral Equations. Preprints. https://doi.org/10.20944/preprints202405.1602.v1
Chicago/Turabian Style
Khansari, A., Mustafa Nouri and Muhammad Arghand. 2024 "An Improved Bernoulli Collocation Method for Solving Volterra Integral Equations" Preprints. https://doi.org/10.20944/preprints202405.1602.v1
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.
Keywords
Bernoulli polynomials; shifted Chebyshev polynomials; Bernoulli collocation method (BCM); Improved Bernoulli collocation method (IBCM); Volterra integral equation s (VIEs)
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
