Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 657–675
Abstract
The aim of this paper is to establish the convergence of a fully discrete Crank-Nicolson type Galerkin scheme for the Cauchy problem associated to the KdV equation. The convergence is achieved for initial data in $L^2$, and we show that the scheme converges strongly in $L^2(0, T; L^2_{loc}(\mathbb{R}))$ to a weak solution for some $T >0$. Finally, the convergence is illustrated by a numerical example.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-458
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 657–675
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Crank-Nicolson scheme KdV equation.