Convergence Analyses of Crank-Nicolson Orthogonal Spline Collocation Methods for Linear Parabolic Problems in Two Space Variables
Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-426
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 58–72
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: parabolic problems orthogonal spline collocation Crank-Nicolson method alternating direction implicit method optimal global error estimates.