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arXiv · 1107.3540

A Haar-type Approximation and a New Numerical Schema for the Korteweg-de Vries Equation

Jason Baggett·Odile Bastille·Alexei Rybkin
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Abstract

We discuss a new numerical schema for solving the initial value problem for the Korteweg-de Vries equation for large times. Our approach is based upon the Inverse Scattering Transform that reduces the problem to calculating the reflection coefficient of the corresponding Schr\"odinger equation. Using a step-like approximation of the initial profile and a fragmentation principle for the scattering data, we obtain an explicit recursion formula for computing the reflection coefficient, yielding a high resolution KdV solver. We also discuss some generalizations of this algorithm and how it might be improved by using Haar and other wavelets.

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Jason Baggett, Odile Bastille, Alexei Rybkin. 2011-07-18. A Haar-type Approximation and a New Numerical Schema for the Korteweg-de Vries Equation. https://arxiv.org/abs/1107.3540

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