Multigrid-sinc methods

摘要

A Galerkin method using Whittaker cardinal or “sinc” functions as basis functions is described for the solution of boundary value problems. When the solution is analytic in the interior of the domain, the error of approximation using 2N + 1 points is O(e−γN12) even if derivatives of the solution are singular at the boundaries. A multigrid method with overall complexity O(NlogN) is used to solve the discrete equations. This paper contains a description of the multigrid-sinc algorithm along with some preliminary numerical results for two-point boundary value problems.