Locally Linearized Runge Kutta method of Dormand and Prince

Abstract

In this paper, the effect that produces the Local Linearization of the embedded Runge–Kutta formulas of Dormand and Prince for initial value problems is studied. For this, embedded Locally Linearized Runge–Kutta formulas are defined and their performance is analyzed by means of exhaustive numerical simulations. For a variety of well-known test equations with different dynamics, the simulation results show that the locally linearized formulas exhibit significant higher accuracy than the original ones, which implies a substantial reduction of the number of time steps and, consequently, a sensitive reduction of the overall computational cost of their adaptive implementation.