The orbital dynamics of an artificial satellite in the Earth’s atmosphere is considered. An analytic first-order atmospheric drag theory is developed using Lagrange’s planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a second-order analytical theory, the equations of motion become very complicated to be integrat...

We show that the well-known order reduction phenomenon affecting implicit Runge-Kutta methods does not occur when approximating periodic solutions of the Korteweg-de Vries equation.

In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge–Kutta methods that can be implemented with a low number registers using their Shu–Osher representation. SSP have been studied in literature and stepsize restrictions ensure numerical monotonicity found. However, for some problems, observed are larger than theoretical ones. Aiming at obtaining additional properties ...

We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions stochastic driven by processes that are rougher than a Brownian motion. use Taylor series representation (B-series) both the numerical scheme and solution of equation in order determine conditions guarantee desired local error underlying method. Subsequently, we prove global given rate. In add...