Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles

A complete stability and convergence analysis is given for twoand 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.

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