A fourth order alternating direction method based on the (2, 2) - Padé Approximant

Abstract

The Peaceman-Rachford alternating direction method, based on the (l,l)-Padé approximant to e ^z , is extended to a fourth-order method based on the (2,2)-approximant. The non-commutativity of the matrices involved means that very few rational approximants lead to satisfactory alternating direction methods. The method based on the (2,2)-approximant extends to three-dimensional problems without loss of stability.

Keywords:

• Parabolic equations
• alternating direction
• A.D.I. methods

C.R. Categories:

• G1.8.