A FOURTH-ORDER FINITE DIFFERENCE SOLVER FOR POISSON'S EQUATION VIA THE HALF-SWEEP ARITHMETIC MEAN (HSAM) METHOD

Abstract

The main purpose ofthis paper is to validate the efficiency and accuracy
of the Half-Sweep Arithmetic Mean (HSAM) method using the fourth order
finite difference approximation equation to solve one-dimensional
Poisson's equation. In this paper, we formulate the Full-Sweep and
Half-Sweep Arithmetic Mean methods, namely FSAM and HSAM
respectively. Finally some computational experiments were conducted
to prove that the fourth-order solver using the HSAM methods is
superior to the FSAM method.

Keywords: Half-Sweep Iterative, Arithmetic Mean Algorithm, Fourth-
Order Finite Difference, Poisson's equation