A Note on the Convergence of a Crank-Nicolson Scheme for the KdV Equation

A Note on the Convergence of a Crank-Nicolson Scheme for the KdV Equation

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.