Orthogonal Spline Collocation Laplace-Modified and Alternating-Direction Methods for Parabolic Problems on Rectangles

Bernard Bialecki, Ryan I. Fernandes
1993 Mathematics of Computation  
A complete stability and convergence analysis is given for two-and three-level, piecewise Hermite bicubic orthogonal spline collocation, Laplacemodified and alternating-direction schemes for the approximate solution of linear parabolic problems on rectangles. It is shown that the schemes are unconditionally stable and of optimal-order accuracy in space and time.
doi:10.2307/2153102 fatcat:mi2qloz2irfv7o6k5eidblsetq