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Somayeh Nemati

Somayeh Nemati

Academic rank: Associate Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 01135302419

Research

Title
An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations
Type
JournalPaper
Keywords
Two-dimensional singular Volterra integral equations, Riemann-Liouville integral operator, Modification of hat functions, Operational matrix, Two-dimensional singular Volterra integral equations
Year
2018
Journal Journal of Mathematical Sciences and Modelling
DOI
Researchers Somayeh Nemati

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.