Stability of locally implicit difference schemes for a two-dimensional equation of heat conduction

A stability criterion for a two-layer difference-operator scheme with a non-self-conjugated operator B is applied to a difference scheme with space-variable weight factors for a two-dimensional equation of heat conduction. An operator matrix determining the scheme stability is obtained. A necessary and sufficient stability condition is formulated in terms of the minimum eigenvalue of the matrix. Numerical calculations indicate that, in the region of a small pitch of the three-dimensional grid and a large value of the heat conductivity coefficient, consideration of a locally implicit scheme is sufficient in order to eliminate the effect of these factors on stability. (AIAA)