MUR8: A multirate extension of the eighth-order Dormand-Prince method (Q1372698)

The authors consider systems of ordinary differential equations of the form \(y'=f(y)\), \(y(0)=0\). Multirate numerical methods are designed for problems where a small number of fast changing components restricts the step of standard numerical integrators. In the paper a multirate Runge-Kutta method consisting of a low order component and a component of eighth order is presented. The partitioning into different levels of slow and fast components is obtained automatically during the integration. A numerical example whose code is available on Internet, is also presented.