Study of stability and dynamical properties of Rosenau-Hyman compactons

We use Pade approximants to study numerically the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons. We present a systematic derivation of Pade approximants for calculating the derivatives of smooth functions on an uniform grid and we illustrate our finding by improving upon traditional fourth-order finite-differences formulas. This study is intended as a stepping block towards a systematic numerical study of soliton solutions with a compact support of generalized Korteweg-de Vries equations.