Approximation of Weakly Singular Integral Equations by Sinc Projection Methods

Abstract

In this paper, two numerical schemes for a nonlinear integral equation of Fredholm type with weakly singular kernel are proposed. These numerical methods combine sinc-collocation and sinc-convolution approximations with Newton and steepest descent iterative methods that involve solving a nonlinear system of equations. The convergence rate of the approximation schemes is also analyzed. Numerical experiments have been performed to illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation. The comparison between the schemes indicates that sinc-convolution method is more effective.