Solving two-dimensional non-linear quadratic integral equations of fractional order via operational matrix method
Multidiscipline Modeling in Materials and Structures
ISSN: 1573-6105
Article publication date: 2 September 2019
Issue publication date: 21 October 2019
Abstract
Purpose
The purpose of this paper is to develop a new method based on operational matrices of two-dimensional delta functions for solving two-dimensional nonlinear quadratic integral equations (2D-QIEs) of fractional order, numerically.
Design/methodology/approach
For this aim, two-dimensional delta functions are introduced, and their properties are expressed. Then, the fractional operational matrix of integration based on two-dimensional delta functions is calculated for the first time.
Findings
By applying the operational matrices, the main problem would be transformed into a nonlinear system of algebraic equations which can be solved by using Newton's iterative method. Also, a few results related to error estimate and convergence analysis of the proposed method are investigated.
Originality/value
Two numerical examples are presented to show the validity and applicability of the suggested approach. All of the numerical calculation is performed on a personal computer by running some codes written in MATLAB software.
Keywords
Acknowledgements
The authors would like to express their great appreciation to editor and anonymous reviewers for their valuable comments and constructive suggestions which have helped to improve the quality and presentation of this paper.
Citation
Mirzaee, F. and Alipour, S. (2019), "Solving two-dimensional non-linear quadratic integral equations of fractional order via operational matrix method", Multidiscipline Modeling in Materials and Structures, Vol. 15 No. 6, pp. 1136-1151. https://doi.org/10.1108/MMMS-10-2018-0168
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited