TY - JOUR
T1 - A finite difference scheme for smooth solutions of the general Degasperis–Procesi equation
AU - Noyola Rodriguez, Jesus
AU - Omel'yanov, Georgy
PY - 2020/7/1
Y1 - 2020/7/1
N2 - © 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.
AB - © 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.
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85076798292&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85076798292&origin=inward
U2 - 10.1002/num.22456
DO - 10.1002/num.22456
M3 - Article
SN - 0749-159X
SP - 887
EP - 905
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
ER -