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Operator Splitting Methods for Generalized Korteweg–De Vries Equations

✍ Scribed by Helge Holden; Kenneth Hvistendahl Karlsen; Nils Henrik Risebro

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
303 KB
Volume
153
Category
Article
ISSN
0021-9991

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✦ Synopsis

We apply the method of operator splitting on the generalized Korteweg-de Vries (KdV) equation u t + f (u) x + εu xxx = 0, by solving the nonlinear conservation law u t + f (u) x = 0 and the linear dispersive equation u t + εu 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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