Using Sinc-collocation method for solving weakly singular Fredholm integral equations of the first kind

Abstract

In this paper, Sinc-collocation method is used to approximate the solution of weakly singular nonlinear Fredholm integral equations of the first kind. Some of the important advantages of this method are rate of convergence of an approximate solution and simplicity for performing even in the presence of singularities. The convergence analysis of the proposed method is proved by preparing the theorems which show the errors decay exponentially and guarantee the applicability of that. Finally, several numerical examples are considered to show the capabilities, validity, and accuracy of the numerical scheme.

Keywords:

• First kind Fredholm integral equation
• weakly singular kernel
• Sinc approximation
• collocation method
• convergence analysis

AMS Subject Classifications:

• 65R20
• 45E10

Notes

No potential conflict of interest was reported by the authors.