Mixed Fourier Legendre spectral Galerkin methods for two-dimensional Fredholm integral equations of the second kind

Abstract

In this article, the mixed Fourier Legendre spectral Galerkin (MFLSG) methods are considered to solve the two-dimensional Fredholm integral equations (fies) on the Banach spaces with smooth kernel. The same methods are also considered to find the eigenvalues of the eigenvalue problems (evps) associated with the two-dimensional fies. Making use of these methods, we establish the error between the approximated solution as well as iterated approximate solution versus exact solution for two-dimensional fies in both L2 and L∞ norms. We also establish the error between approximated eigen-values, eigen-vectors and iterated eigen-vectors and exact eigen-elements by MFLSG methods in L2 and L∞ norms. The numerical illustrations are introduced for the error of these methods.