A criterion of asymptotic stability for a difference scheme with alternating weight factors (Q1281217)

A development of A. A. Samarskij's previous works on the investigation of stability and accuracy for difference schemes approximating the heat conduction equation, in particular, is given. It was noted in these works that the use of a stable but not asymptotically stable scheme leads on a long time interval to a full distortion of the solution of the given problem. Necessary and sufficient conditions of asymptotic stability are derived and the asymptotic accuracy of a difference scheme with alternating weights is investigated.