Numerical treatment of singular integral equation in unbounded domain

ABSTRACT

In literature, numerical solutions for the singular integral equation in unbounded domain are rarely investigated. The main motivation of this study is to propose a practical matrix method based on Laguerre functions to approximate the solution of this integral equation. Laguerre functions which are obtained from the Laguerre polynomials are used to avoid fluctuations for large values. The main characteristic of the scheme is good accuracy with two basis functions and less computational cost which are the consequences of Laguerre functions properties and its dual operational matrix. This matrix is equal to the identity matrix which simplify the approximation procedure and reduce the computational error of the scheme. In this technique, dual operational matrix, matrix forms and collocation method are employed to convert singular integral equation into a matrix equation. Convergence analysis and the stability of the proposed method is presented. Some numerical examples with comparison illustrate the efficiency of the scheme.

Keywords:

• Singular integral equation
• Laguerre functions
• dual operational matrix
• convergence analysis and stability

2010 Mathematics Subject Classifications:

• 45E10
• 65R20

Acknowledgments

Authors are very grateful to referees for reading the paper carefully and for comments and suggestions which improved the quality of paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).