Operator Splitting Methods for Generalized Korteweg–De Vries Equations

Author: Holden H.   Karlsen K.H.   Risebro N.H.  

Publisher: Academic Press

ISSN: 0021-9991

Source: Journal of Computational Physics, Vol.153, Iss.1, 1999-07, pp. : 203-222

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Abstract

We apply the method of operator splitting on the generalized Korteweg--de Vries (KdV) equation ut+f(u)xuxxx=0, by solving the nonlinear conservation law ut+f(u)x=0 and the linear dispersive equation utuxxx=0 sequentially. We prove that if the approximation obtained by operator splitting converges, then the limit function is a weak solution of the generalized KdV equation. Convergence properties are analyzed numerically by studying the effect of combining different numerical methods for each of the simplified problems.

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