Conservative finite difference schemes for the Degasperis-Procesi equation

A Conservative Discontinuous Galerkin Method for the Degasperis–procesi Equation

In this work, we design, analyze and test a conservative discontinuous Galerkin method for solving the Degasperis–Procesi equation. This model is integrable and admits possibly discontinuous solutions, and therefore suitable for modeling both short wave breaking and long wave propagation phenomena. The proposed numerical method is high order accurate, and preserves two invariants, mass and ener...

Numerical Schemes for Computing Discontinuous Solutions of the Degasperis-procesi Equation

Recent work [4] has shown that the Degasperis-Procesi equation is well-posed in the class of (discontinuous) entropy solutions. In the present paper we construct numerical schemes and prove that they converge to entropy solutions. Additionally, we provide several numerical examples accentuating that discontinuous (shock) solutions form independently of the smoothness of the initial data. Our fo...

Global Existence and Blow-up Phenomena for a Weakly Dissipative Degasperis-procesi Equation

This paper is concerned with the long time behaviour of a weakly dissipative Degasperis-Procesi equation. Our analysis discloses the co-existence of global in time solutions and finite time break down of strong solutions. Our blow-up criterion for the initial profile generalizes considerably results obtained earlier in [32].

A study on Degasperis - Procesi equation by iterative methods

On Time Fractional Modifed Camassa-Holm and Degasperis-Procesi Equations by Using the Haar Wavelet Iteration Method

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...