REGULAR JOURNAL PAPER Convergence of sinc approximation for Fredholm integral equation with degenerate kernel K. Maleknejad School of Mathematics, Iran University of Science & Technology Narmak, Tehran, Iran M. Alizadeh Department of Mathematics, Faculty of Science, Islamic Azad University, Karaj Branch, Karaj, Iran, and R. Mollapourasl Department of Mathematics, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran Abstract Purpose – The purpose of this paper is to discuss a numerical method for solving Fredholm integral equations of the first kind with degenerate kernels and convergence of this numerical method. Design/methodology/approach – By using sinc collocation method in strip, the authors try to estimate a numerical solution for this kind of integral equation. Findings – Some numerical results support the accuracy and efficiency of the stated method. Originality/value – The paper presents a method for solving first kind integral equations which are ill-posed. Keywords Mathematics, Integral equations, Integral equation of the first kind, Collocation method, Sinc approximation, Clenshaw-Curtis quadrature Paper type Research paper 1. Introduction The purpose of this paper is to develop a high order numerical method for Fredholm integral equation of the first kind defined by: Z b a kðs; t Þf ðtÞdt ¼ gðsÞ 2 1 , a # s # b , 1 ð1Þ where k(s, t) and g(s) are known functions and f (t) is the solution to be determined. In this equation k (s, t) is called kernel of integral equation. We can write equation (1) as: Kf ¼ g The current issue and full text archive of this journal is available at www.emeraldinsight.com/0368-492X.htm K 41,3/4 482 Kybernetes Vol. 41 No. 3/4, 2012 pp. 482-490 q Emerald Group Publishing Limited 0368-492X DOI 10.1108/03684921211229532