Abstract: In this paper, the formulation of a new group explicit
method with a fourth order accuracy is described in solving the two
dimensional Helmholtz equation. The formulation is based on the
nine-point fourth order compact finite difference approximation
formula. The complexity analysis of the developed scheme is also
presented. Several numerical experiments were conducted to test the
feasibility of the developed scheme. Comparisons with other existing
schemes will be reported and discussed. Preliminary results indicate
that this method is a viable alternative high accuracy solver to the
Helmholtz equation.
Abstract: We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.