The Sinc-Galerkin Method for Fourth-Order Differential Equations

Abstract

The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $O(e^{ - \kappa \sqrt M } )$ is carefully developed and the special features of the discrete system are described. Spectral properties and conditioning of the associated matrices are given. The appropriate choice of weight function in the Galerkin inner product is discussed with primary emphasis given to choices that are best suited to fourth-order partial differential equations. Numerical results are included to help illustrate the parameter selections made and confirm the efficiency and accuracy of the method.