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Survey of numerical methods for the Korteweg de Vries equation.

Haugen, Øystein Storaas
Master thesis
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URI
http://hdl.handle.net/11250/258277
Date
2009
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  • Institutt for matematiske fag [1390]
Abstract
Numerical methods for solving The Korteweg-de Vries (KdV) equation are studied. Four main classes of numerical methods were implemented and tested; a semi-discretized finite difference method, an iterating finite difference method suggested by Yoshinori Kametaka, the Fourier spectral method and an split-step method. The methods are compared to true solutions for error calculations. The error are discussed both as a function of computational time on a reference computer and as a function of grid points. The methods are also tested on initial conditions who does not have known solutions. The convergence rate and complexity of the implementation are also discussed.
Publisher
Institutt for matematiske fag

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