Numerical solutions for Fredholm integral equations of the second kind with weakly singular kernel using spectral collocation method

摘要

We investigate the spectral collocation for Fredholm integral equations of the second kind with weakly singular kernel. The Jacobi-Gauss quadrature formula is used to approximate the integral operator in the numerical implementation. We obtain the convergence rates for the approximated solution of weakly singular Fredholm integral equations, which show that the errors of the approximate solution decay exponentially in L∞-norm and weighted L2-norm. Some numerical examples are given to illustrate the theoretical results.