Numerically induced phase shift in the KdV soliton
Journal of Computational Physics
A finite difference scheme for the K(2, 2) compacton equation
Journal of Computational Physics
A numerical study of compactons
Mathematics and Computers in Simulation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Asymptotic analysis of the lattice Boltzmann equation
Journal of Computational Physics
Padé numerical method for the Rosenau-Hyman compacton equation
Mathematics and Computers in Simulation
Self-similar radiation from numerical Rosenau-Hyman compactons
Journal of Computational Physics
Hi-index | 31.45 |
Compacton propagation under dissipation shows amplitude damping and the generation of tails. The numerical simulation of compactons by means of dissipative schemes also show the same behaviors. The truncation error terms of a numerical method can be considered as a perturbation of the original partial differential equation and perturbation methods can be applied to its analysis. For dissipative schemes, or when artificial dissipation is added, the adiabatic perturbation method yields evolution equations for the amplitude loss in the numerical solution and the amplitude of the numerically-induced tails. In this paper, such methods are applied to the K(2,2) Rosenau-Hyman equation, showing a very good agreement between perturbative and numerical results.