Year: 2021
Author: Bernard Bialecki, Ryan I. Fernandes
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 620–641
Abstract
For the heat equation on a rectangle and nonzero Dirichlet boundary conditions, we consider an ADI orthogonal spline collocation method without perturbation terms, to specify boundary values of intermediate solutions at half time levels on the vertical sides of the rectangle. We show that, at each time level, the method has optimal convergence rate in the $L^2$ norm in space. Numerical results for splines of orders 4, 5, 6 confirm our theoretical convergence rates and demonstrate suboptimal convergence rates in the $H^1$ norm. We also demonstrate numerically that the scheme without the perturbation terms is applicable to variable coefficient problems yielding the same convergence rates obtained for the heat equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19385
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 620–641
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Convergence alternating direction implicit method orthogonal spline collocation perturbation terms.