Explicit group versus implicit line iterative methods

Abstract

In this paper, a new explicit 4 point and 9 point block overrelaxation scheme for the numerical solution of the sparse linear systems derived from the discretisation of self-adjoint elliptic partial differential equations by finite difference/element techniques. A comparison with the implicit 1-line and 2‐line block S.O.R. schemes for the model problem clearly demonstrates the new techniques to be computationally superior.

Keywords:

• 4 point and 9 point explicit block schemes
• 1 line and 2 line implicit schemes
• S.O.R
• elliptic P.D.E.'s

C.R. Categories::

• G.1.3
• G.1.8

Now at the University of Texas at San Antonio, San Antonio, Texas 78285, U.S.A

Now at the University of Texas at San Antonio, San Antonio, Texas 78285, U.S.A

Notes

Now at the University of Texas at San Antonio, San Antonio, Texas 78285, U.S.A