A Method to Approximate Solution of the First Kind Abel Integral Equation Using Navot's Quadrature and Simpson's Rule

Subject Areas : International Journal of Industrial Mathematics

M. A. Fariborzi Araghi ¹ , S. Yazdani ²

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, P.O. Box 13185.768, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, P.O. Box 13185.768, Tehran, Iran

Received: 2013-11-03 Accepted : 2013-11-03 Published : 2009-01-01

Keywords:

Abstract :

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this kind of integral equation is proposed, thenthe convergence of algorithm is derived. Some numerical results show the eciency of thementioned method.