Abstract—A collocation method based on quintic B-spline is presented for the numerical solution of Abel's integral equation. The solution is collocated by quintic B-spline and then the integral equation is approximated by the product trapezoidal formula. The error analysis of proposed numerical scheme is studied theoretically. The presented method is tested with two examples and numerical results are given to illustrate the efficiency of the proposed method.

Index Terms—Abel's integral equation, quintic B-spline, product trapezoidal, error analysis.

Zahra Mahmoodi is with the Department of Mathematics, Abhar Branch, Islamic Azad University, Abhar, Iran (email: z_mahmoodi_a@yahoo.com).

Cite: Zahra Mahmoodi, "Quintic B-Spline Collocation for Solving Abel's Integral Equation," International Journal of Applied Physics and Mathematics vol. 5, no. 4, pp. 243-251, 2015.