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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@Article{IJNAM-13-58, author = {M. Khebchareon, A. K. Pani and G. Fairweather}, title = {Convergence Analyses of Crank-Nicolson Orthogonal Spline Collocation Methods for Linear Parabolic Problems in two Space Variables}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {58--72}, 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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/426.html} }
TY - JOUR T1 - Convergence Analyses of Crank-Nicolson Orthogonal Spline Collocation Methods for Linear Parabolic Problems in two Space Variables AU - M. Khebchareon, A. K. Pani & G. Fairweather JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 58 EP - 72 PY - 2016 DA - 2016/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/426.html KW - parabolic problems KW - orthogonal spline collocation KW - Crank-Nicolson method KW - alternating direction implicit method KW - optimal global error estimates AB - 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.
M. Khebchareon, A. K. Pani & G. Fairweather. (1970). Convergence Analyses of Crank-Nicolson Orthogonal Spline Collocation Methods for Linear Parabolic Problems in two Space Variables. International Journal of Numerical Analysis and Modeling. 13 (1). 58-72. doi:
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