An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations

Authors : Somayeh NEMATİ

Pages : 192-201

Doi:10.33187/jmsm.423059

View : 22 | Download : 8

Publication Date : 2018-12-30

Article Type : Research Paper

Abstract :In this paper, we consider a spectral method to solve a class of two-dimensional singular Volterra integral equations using some basic concepts of fractional calculus. This method uses a modification of hat functions for finding a numerical solution of the considered equation. Some properties of the modification of hat functions are presented. The main contribution of this work is to introduce the fractional order operational matrix of integration for the considered basis functions. Making use of the Riemann-Liouville fractional integral operator helps us to reduce the main problem to a system of linear algebraic equations which can be solved easily. After that, error analysis of the method is discussed. Finally, numerical examples are included to confirm the accuracy and applicability of the suggested method.
Keywords : Two dimensional singular Volterra integral equations, Riemann Liouville integral operator, Modification of hat functions, Operational matrix, Two dimensional singular Volterra integral equations