A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel

作者：Rebelo Magda; Diogo Teresa^*

来源：Journal of Computational and Applied Mathematics, 2010, 234(9): 2859-2869.

DOI：10.1016/j.cam.2010.01.034

• Nonlinear integral equation
• Weakly singular kernel
• Hybrid collocation method

This work is concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation. Owing to I he singular behavior of the solution near the origin, the global convergence order of product integration and collocation methods is not optimal. In order to recover the optimal orders a hybrid collocation method is used which combines a non-polynomial approximation on the first subinterval followed by piecewise polynomial collocation on a graded mesh. Some numerical examples are presented which illustrate the theoretical results and the performance of the method. A comparison is made with the standard graded collocation method.

• 出版日期2010-9-1