Discrete Legendre multi-projection methods for Fredholm integral equations of the second kind and the corresponding eigenvalue problem

摘要

In this paper, the discrete multi-projection methods are proposed to solve Fredholm integral equations of the second kind with the corresponding eigenvalue problem using Legendre polynomial bases. The error bounds for the approximate, iterated approximate solutions for Fredholm integral equations of the second kind are evaluated using sufficiently accurate numerical quadrature rule. It has been shown that iterated Legendre multi-Galerkin solution converges faster than Legendre multi-Galerkin solutions in both infinity and $L^2$-norm and Legendre multi-projection method converges faster than Legendre projection method. The convergence rates for approximated eigenelements in Legendre multi-projection methods also have been evaluated. Numerical examples are presented to validate the theoretical estimates for both the problems.