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Numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types)

Jiao Wang (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 9 April 2021

Issue publication date: 22 September 2021

211

Abstract

Purpose

This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types).

Design/methodology/approach

The main idea of the presented algorithm is to combine Bernoulli polynomials approximation with Caputo fractional derivative and numerical integral transformation to reduce the studied two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations to easily solved algebraic equations.

Findings

Without considering the integral operational matrix, this algorithm will adopt straightforward discrete data integral transformation, which can do good work to less computation and high precision. Besides, combining the convenient fractional differential operator of Bernoulli basis polynomials with the least-squares method, numerical solutions of the studied equations can be obtained quickly. Illustrative examples are given to show that the proposed technique has better precision than other numerical methods.

Originality/value

The proposed algorithm is efficient for the considered two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations. As its convenience, the computation of numerical solutions is time-saving and more accurate.

Keywords

Citation

Wang, J. (2021), "Numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types)", Engineering Computations, Vol. 38 No. 9, pp. 3548-3563. https://doi.org/10.1108/EC-06-2020-0353

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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