Pn. Vabishchevich et al., DIFFERENCE-SCHEMES WITH VARIABLE WEIGHTS FOR EVOLUTIONARY EQUATIONS OF THE 2ND-ORDER, Doklady Akademii nauk BSSR, 38(3), 1994, pp. 13-15
Operator-difference schemes with variable (including discontinuous) we
ights for approximate solution finding of Cauchy problem for evolution
al equation's of the second order are constructed in the present paper
. The sufficient conditions that correspond to stability with respect
to initial data and right sides for the main two versions of schemes w
ith weights are obtained. Our research is based on Samarskii general t
heory of the difference schemes stability.