Preprint 1999-003

Operator Splitting Methods for Generalized Korteweg-de Vries Equations

Helge Holden, Kenneth Hvistendahl Karlsen, and Nils Henrik Risebro

Abstract: We apply the method of operator splitting on the generalized Korteweg--de Vries (KdV) equation $u_{t}+f(u)_{x} +\eps u_{xxx} = 0$, by solving the nonlinear conservation law $u_{t}+f(u)_{x}=0$ and the linear dispersive equation $u_{t}+\eps u_{xxx} = 0$ 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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Helge Holden, <>
Kenneth Hvistendahl Karlsen, <>
Nils Henrik Risebro, <>
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<> March 5 1999.

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