# Approximation of Weakly Singular Integral Equations by Sinc Projection Methods

## TL;DR

This paper introduces two sinc-based numerical schemes for solving nonlinear Fredholm integral equations with weakly singular kernels, analyzing their convergence and effectiveness through numerical experiments.

## Contribution

It proposes and compares sinc-collocation and sinc-convolution methods combined with iterative solvers for weakly singular integral equations.

## Key findings

- Sinc-convolution method is more effective than sinc-collocation.
- Convergence rates are established and validated numerically.
- Solution sensitivity to parameters is analyzed.

## 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.