Numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types). Issue 9 (9th April 2021)

• Record Type: Journal Article
• Authors: Wang, Jiao
• Is Part Of: Engineering computations. Volume 38:Issue 9(2021)
• Page Start: 3548
• Page End: 3563
• Publication Date: 2021-04-09
• Subjects: Caputo fractional derivative -- Numerical solutions -- Least-squares method -- Bernoulli basis polynomials -- Two-dimensional nonlinear Volterra-Fredholm type equations; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-06-2020-0353
• Languages: English
• ISSNs: 0264-4401

Abstract

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.