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

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.

65M15, 65M70

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@Article{IJNAM-13-58, author = {}, 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 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, orthogonal spline collocation, Crank-Nicolson method, alternating direction implicit method, 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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