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arXiv · 1408.3552

Convergence of a higher-order scheme for Korteweg-de Vries equation

Rajib Dutta·Ujjwal Koley·Nils Henrik Risebro
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Abstract

We study the convergence of higher order schemes for the Cauchy problem associated to the KdV equation. More precisely, we design a Galerkin type implicit scheme which has higher order accuracy in space and first order accuracy in time. The convergence is established for initial data in L^2, and we show that the scheme converges strongly in L^2(0,T; L^2_loc(\R)) to a weak solution. Finally, the convergence is illustrated by several examples.

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Rajib Dutta, Ujjwal Koley, Nils Henrik Risebro. 2014-08-15. Convergence of a higher-order scheme for Korteweg-de Vries equation. https://arxiv.org/abs/1408.3552

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