On a class of vector additive difference schemes (Q1842492)

The Cauchy problem \(dy/dt + Ay = 0\), \(y(0) = y_ 0\), where \(A\) (positive, self-conjugate) has an additive representation, is considered. A transformation to a symmetric vector problem is given, which allows to construct vector additive difference schemes. Two- and three-layer difference schemes are investigated and, for regularized difference schemes using the additive structure of \(A\), stability conditions are given.