^{}Department of Mathematics,College of basic science, Islamic Azad University, Alborz, Iran.

Abstract

We have developed a three level implicit method for solution of the Helmholtz
equation. Using the cubic spline in space and nite dierence in time directions. The approach
has been modied to drive Numerov type nite dierence method. The method yield the tri-
diagonal linear system of algebraic equations which can be solved by using a tri-diagonal
solver. Stability and error estimation of the presented method are analyzed.The obtained
results satised the ability and eciency of the method.