A finite difference scheme for smooth solutions of the general Degasperis–Procesi equation

Jesus Noyola Rodriguez, Georgy Omel'yanov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

© 2019 Wiley Periodicals, Inc. The general Degasperis–Procesi equation (gDP) describes the evolution of the water surface in a unidirectional shallow water approximation. We propose a finite-difference scheme for this equation that preserves some conservation and balance laws. In addition, the stability of the scheme and the convergence of numerical solutions to exact solutions for solitons are proved. Numerical experiments confirm the theoretical conclusions. For essentially nonintegrable versions of the gDP equation, it is shown that solitons and antisolitons collide almost elastically: they retain their shape after interaction, but a small “tail”, the so-called “radiation”, appears.
Original languageAmerican English
Pages (from-to)887-905
Number of pages19
JournalNumerical Methods for Partial Differential Equations
DOIs
StatePublished - 1 Jul 2020

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