A fast multiscale Galerkin method for solving second order linear Fredholm integro-differential equation with Dirichlet boundary conditions

Abstract

In this paper, a fast multiscale Galerkin method is developed for solving second order linear Fredholm integro-differential equation with Dirichlet boundary conditions. The method is based on a matrix truncation strategy which leads to generating coefficient matrix rapidly. We prove that the method is stable and has an optimal convergence order and nearly linear computational complexity (up to a logarithmic factor). Numerical examples are presented to illustrate its computational efficiency, approximation accuracy and theoretical results, and to compare the computed results with those of the original multiscale Galerkin method proposed recently by the same authors.