SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION

Abstract

We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation order. The schemes are compared with the standard five-point pointwise representation, which has second-order accurate local truncation error and a nine-point fourth-order local truncation error scheme based on a Padé approximation. Numerical results are presented for a model problem.