Numerical methods based on modified equations for nonlinear evolution equations with compactons

Compactons are traveling wave solutions with compact support resulting from the balance of both nonlinearity and nonlinear dispersion. Numerical methods with second-, fourth-, sixth-, and eighth-order approximations to the spatial derivatives obtained by means of the method of modified equations applied to the Ismail–Taha finite difference scheme for the Rosenau–Hyman equation are developed. The whole set of methods is compared among them in accuracy, invariant conservation, and in compacton collisions. The best method, among those studied, in terms of the tradeoff between accuracy and computational cost is determined.