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

2014/08/15 by Rajib Dutta, Dutta, Rajib, Ujjwal Koley +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1408.3552

openalex publication_date 2014/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L², and we show that the scheme converges strongly in L²(0,T; L²_loc(\R)) to a weak solution. Finally, the convergence is illustrated by several examples.

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