Preprint 1999003
Operator Splitting Methods for
Generalized Kortewegde Vries Equations
Helge Holden, Kenneth Hvistendahl Karlsen, and Nils Henrik Risebro
Abstract:
We apply the method of operator splitting on the
generalized Kortewegde 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.
 Paper:
 Available as PostScript.
 Author(s):
 Helge Holden,
<holden@math.ntnu.no>
 Kenneth Hvistendahl Karlsen,
<kennethk@mi.uib.no>
 Nils Henrik Risebro,
<nilshr@math.uio.no>
 Publishing information:

 Comments:

 Submitted by:

<holden@math.ntnu.no>
March 5 1999.
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Last modified: Wed Apr 14 08:51:25 1999