@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} }