Stability boundaries of some two - and three-level difference schemes
by
Alexei V. Goolin
M. V. Lomonosov Moscow State University

The review of some new results in the stability theory of operator-difference schemes in Euclidean spaces is represented. As a roole the schemes with operator weights are discussed, namely two-level schemes

\frac yn+1-yn\tau+\sigmaAyn+1+(I-\sigma) Ayn=0,   n=0,  1,  . . .     y0 specified,

and symmetrical three-level schemes

\frac yn+1-2yn+yn-1\tau2 +\sigmaAyn+1+(I-2\sigma) Ayn+\sigmaAyn-1=0,

n=1,  2,  . . .     y₀ , y₁ specified,

where A ¨ \sigma are linear operators in the Euclidean space H. The main problems discussed in the reports are following.

1. Theorems concerning norm-invariant stability criterions with respect to initial data.

2. Numerical obtaining of stability boundaries in the plane of grid parameters for spatially two-dimensional difference schemes with variable weights.

Date received: February 16, 2000