HIGH-ORDER FINITE-DIFFERENCE METHODS FOR THE HELMHOLTZ-EQUATION

High-order finite difference methods for solving the Helmholtz equatio n are developed and analyzed, in one and two dimensions on uniform gri ds. The standard pointwise representation has a second-order accurate local truncation error. We also study two schemes which have a fourth- order accurate local truncation error. One of the high-order schemes i s based on generalizations of the Pade approximation. The second schem e is based on high-order approximation to the derivative calculated fr om the Helmholtz equation itself. A symmetric high-order representatio n is developed for a Neumann boundary condition. Numerical results are presented on model problems approximated with the developed schemes. (C) 1998 Elsevier Science S.A. All rights reserved.