Removing trailing tails and delays induced by artificial dissipation in Padé numerical schemes for stable compacton collisions
For researchers simulating compacton collisions, this method eliminates undesirable artifacts from artificial dissipation, improving accuracy in a specific domain.
The paper addresses trailing tails, amplitude damping, and delays caused by artificial dissipation in Padé numerical schemes for simulating compacton collisions in the Rosenau-Hyman K(n,n) equation. By counterbalancing two sources of dissipation using adiabatic perturbation methods, tails are completely removed with only a small compact ripple remaining, preserving numerical stability.
The numerical simulation of colliding solitary waves with compact support arising from the Rosenau-Hyman K(n,n) equation requires the addition of artificial dissipation for stability in the majority of methods. The price to pay is the appearance of trailing tails, amplitude damping, and delays as the solution evolves. These undesirable effects can be corrected by properly counterbalancing two sources of artificial dissipation; this procedure is designed by using the slow time evolution of the parameters of the solitary waves under the presence of the dissipation determined by means of adiabatic perturbation methods. The validity of the tail removal methodology is demonstrated on a Padé numerical scheme. The tails are completely removed leaving only a small compact ripple at the original position of their front, and the numerical stability of the scheme under compacton collisions is preserved, as shown by extensive numerical experiments for several values of n.