CONVERGENCE ANALYSES OF CRANK-NICOLSON ORTHOGONAL SPLINE COLLOCATION METHODS FOR LINEAR PARABOLIC PROBLEMS IN TWO SPACE VARIABLES

摘要

The Crank-Nicolson (CN) orthogonal spline collocation method and its alternating direction implicit (ADI) counterpart are considered for the approximate solution of a class of linear parabolic problems in two space variables. It is proved that both methods are second order accurate in time and of optimal order in certain H-j norms in space. Also, L-infinity estimates in space are derived.