An eight-order accurate numerical method for the solution of 2D Helmholtz equation

摘要

This note is concerned with a numerical method for the solution of 2D Helmholtz equation in unit square. The method uses a finite difference approximation in one coordinate space. Similar to the method of line, the method treats the working equation as a system of ordinary differential equation in the remaining independent variable. The method uses a coordinate transformation to decouple the system of ODE. Using this procedure, it is possible to formulate numerical schemes with arbitrary orders of accuracy. Numerical results for an eight-order accurate are presented.