Explicit Runge–Kutta pairs appropriate for engineering applications

Abstract

Runge–Kutta (RK) pairs of orders seven and five with minimal phase lag are derived for the numerical approximation of ordinary differential equations with engineering applications. For a class of initial value problems, whose solution is known to be described by free oscillations or free oscillations of high frequency with forced oscillations of low frequency superimposed, the new pair seem to offer clear advantages with respect to older pairs. The new pair is much more efficient than methods using the same number of stages, when applied in some problems of the plate deflection, the wave equation or vibratory systems.