A spectral method for the solution of boundary value problems

摘要

A new numerical method to solve two-point boundary value problems for second order differential equations is proposed. This method is based on the singular value expansion of an integral formulation of the derivative operator. Here, we outline such an expansion and we propose a method to build new algebraic schemes able to solve boundary value problems.The performances of the presented method are tested by numerical experiments on boundary value problems that have known solutions.