Two-dimensional shifted Legendre polynomials operational matrix method for solving the two-dimensional integral equations of fractional order

Esmail Hesameddini and Mehdi Shahbazi

Applied Mathematics and Computation, 2018, vol. 322, issue C, 40-54

Abstract: This work approximates the unknown functions based on the two-dimensional shifted Legendre polynomials operational matrix method (2D-SLPOM) for the numerical solution of two-dimensional fractional integral equations. The present method reduces these equations to a system of algebraic equations and then this system will be solved numerically by Newton’s method. Moreover, an estimation of the error bound for this algorithm will be shown by preparing some theorems. Some examples are presented to demonstrate the validity and applicability of the proposed method with respect to the two-dimensional block pulse functions method (2D-BPFs) and two-dimensional Bernstein polynomials operational matrix method (2D-BPOM).

Keywords: Two-dimensional shifted Legendre polynomials; Two-dimensional fractional integral equations; Error estimate; Numerical algorithm (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:322:y:2018:i:c:p:40-54

DOI: 10.1016/j.amc.2017.11.024

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