Some modified Runge-Kutta methods for the numerical solution of initial-value problems with oscillating solutions
In the numerical modelling of oscillatory problems, the phase shift introduced by a numerical scheme is an important attribute in assessing its quality. Thus, methods with high phase-lag order, along with moderately high classical order are sought. This paper introduces two new explicit Runge-Kutta methods with order 5 and phase-lag orders 10 and 12, respectively. The author proposes an embedding scheme where phase-lag is estimated and used for error control.
scientific article; zbMATH DE number 1204428