Volume 13, Issue 1
Convergence Analyses of Crank-Nicolson Orthogonal Spline Collocation Methods for Linear Parabolic Problems in two Space Variables

M. Khebchareon, A. K. Pani & G. Fairweather

DOI:

Int. J. Numer. Anal. Mod., 13 (2016), pp. 58-72

Published online: 2016-01

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  • Abstract

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^∞ estimates in space are derived.

  • Keywords

parabolic problems orthogonal spline collocation Crank-Nicolson method alternating direction implicit method optimal global error estimates

  • AMS Subject Headings

65M15 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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