The stability of locally implicit difference schemes for the two-dimensional heat-conduction equation

A stability criterion for a two-layer operator difference scheme with non-self-conjugate operator B is applied to a difference scheme with weight multipliers which vary in space for the two-dimensional heat-conduction equation. The matrix of the operator governing the stability of the scheme is obtained. A necessary and sufficient condition for stability is formulated in terms of the minimum eigenvalue of that matrix. It is shown in numerical calculations that the influence of a small spatial step and large thermal conductivity on the stability condition can be eliminated by the use of a locally implicit scheme. Copyright (C) 1996 Elsevier Science Ltd.