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

Somayeh Nemati

doi:10.33187/jmsm.423059

EN

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

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

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Somayeh Nemati ^*
0000-0003-1724-6296
Iran

Publication Date

December 30, 2018

Submission Date

May 12, 2018

Acceptance Date

November 3, 2018

Published in Issue

Year 2018 Volume: 1 Number: 3

DOI

https://doi.org/10.33187/jmsm.423059

IZ

https://izlik.org/JA37EM58SC

APA

Nemati, S. (2018). An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations. Journal of Mathematical Sciences and Modelling, 1(3), 192-201. https://doi.org/10.33187/jmsm.423059

AMA

1.Nemati S. An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations. Journal of Mathematical Sciences and Modelling. 2018;1(3):192-201. doi:10.33187/jmsm.423059

Chicago

Nemati, Somayeh. 2018. “An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations”. Journal of Mathematical Sciences and Modelling 1 (3): 192-201. https://doi.org/10.33187/jmsm.423059.

EndNote

Nemati S (December 1, 2018) An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations. Journal of Mathematical Sciences and Modelling 1 3 192–201.

IEEE

[1]S. Nemati, “An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 3, pp. 192–201, Dec. 2018, doi: 10.33187/jmsm.423059.

ISNAD

Nemati, Somayeh. “An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations”. Journal of Mathematical Sciences and Modelling 1/3 (December 1, 2018): 192-201. https://doi.org/10.33187/jmsm.423059.

JAMA

1.Nemati S. An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations. Journal of Mathematical Sciences and Modelling. 2018;1:192–201.

MLA

Nemati, Somayeh. “An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 3, Dec. 2018, pp. 192-01, doi:10.33187/jmsm.423059.

Vancouver

1.Somayeh Nemati. An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations. Journal of Mathematical Sciences and Modelling. 2018 Dec. 1;1(3):192-201. doi:10.33187/jmsm.423059