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 - <p style="text-align: justify;">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.</p>