DISCRETE-TIME ORTHOGONAL SPLINE COLLOCATION METHODS FOR SCHRODINGER-EQUATIONS IN 2 SPACE VARIABLES

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrodinger equati on in two space variables. These are Crank-Nicolson and alternating di rection implicit (ADI) schemes employing C-1 piecewise polynomial spac es of arbitrary degree greater than or equal to 3 in each space variab le. The stability of the schemes is examined and optimal order a prior i L-2- and H-1-error estimates at each time step are derived. Parallel implementation of the ADI scheme is discussed.