Approximate Solutions of Cauchy type Singular...

Approximate Solutions of Cauchy type Singular Integral Equations

Author Name : Srikumar Panda

ABSTRACT An approximate method is developed for the numerical solution of singular integral equation of the first kind involving Cauchy-type singular kernel. In this study trapezoidal rule has been used to approximate the integral of the singular integral equation, which leads to an over-determined system of linear algebraic equations involving the unknowns. By employing Newton’s method followed by least-squares method, the solution of the over-determined system is obtained. To check the accuracy and efficiency of the proposed approximate method, it is applied to solve different examples with known exact solutions. The numerical solutions obtained here confirm the validity of the proposed method. The present study proposed an interesting and viable alternative to existing numerical methods for solving Cauchy type singular integral equation. Keywords: Singular integral equation; Cauchy-type kernel; Newton’s method; Over-determined system; Leastsquares method; Numerical solution AMS Subject Classification: 45B05, 45E05