STABLE EXPLICIT SCHEMES FOR EQUATIONS OF THE SCHROEDINGER TYPE.

Most conventional explicit finite difference schemes, e. g. Euler's scheme, for solving the parabolic equation of Schroedinger type u//t equals iu//x//x are unconditionally unstable. This difficulty can be overcome by introducing a dissipative term to the conventional explicit schemes. Based on this approach, we derive a class of new explicit finite difference schemes which are conditionally stable, spans two time levels and are O(k, h**2) accurate. We also determine the schemes from this class that have the least restrictive stability requirements. It is interesting to note that the analog of the Lax-Wendroff scheme is unstable.