Stability criteria for finite difference approximations to parabolic systems

The purpose of this note is to provide a brief account of several recent results regarding L-2-stability of a well-known family of finite difference approximations to the initial value problem associated with the Petrowski well-posed, multispace-dimensional parabolic system partial derivative u(x, t)/partial derivative t = Sigma(1 less than or equal to p less than or equal to q less than or equal to s) A(pq) partial derivative(2)u(x, t)/partial derivative x(p)partial derivative x(q) + Sigma(1 less than or equal to p less than or equal to s) B-p partial derivative u(x, t)/partial derivative x(p) + Cu(x, t), where A(pq), B-p and C are constant matrices, A(pq) being Hermitian. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.