Removing trailing tails and delays induced by artificial dissipation in Padé numerical schemes for stable compacton collisions

摘要

The numerical simulation of colliding solitary waves with compact supportarising from the Rosenau-Hyman K(n,n) equation requires the addition ofartificial dissipation for stability in the majority of methods. The price topay is the appearance of trailing tails, amplitude damping, and delays as thesolution evolves. These undesirable effects can be corrected by properlycounterbalancing two sources of artificial dissipation; this procedure isdesigned by using the slow time evolution of the parameters of the solitarywaves under the presence of the dissipation determined by means of adiabaticperturbation methods. The validity of the tail removal methodology isdemonstrated on a Pad'e numerical scheme. The tails are completely removedleaving only a small compact ripple at the original position of their front,and the numerical stability of the scheme under compacton collisions ispreserved, as shown by extensive numerical experiments for several values of n.