A unified spectral collocation method for nonlinear systems of multi-dimensional integral equations with convergence analysis

摘要

The main purpose of this paper is to construct and analyze a spectral collocation method for solving a general class of nonlinear systems of multi-dimensional integral equations. In order to obtain high-order accuracy for the approximation, the integral terms in the resulting equation are approximated by using the Legendre spectral quadrature rule. The spectral rate of convergence for the proposed method is established in the L~2-norm showing that the error of approximate solution decays exponentially. Numerical examples are presented to confirm this theoretical prediction.