Multirate linear multistep methods

The design of a code which uses different stepsizes for different components of a system of ordinary differential equations is discussed. Methods are suggested which achieve moderate efficiency for problems having some components with a much slower rate of variation than others. Techniques for estimating errors in the different components are analyzed and applied to automatic stepsize and order control. Difficulties, absent from non-multirate methods, arise in the automatic selection of stepsizes, leading to a suggested organization of the code that is counter-intuitive. An experimental code and some initial experiments are described.Dedicated to Professor Germund Dahlquist on the occasion of his 60th birthdaySupported in part by the Department of Energy under grant DOE DEAC0276ERO2383.Work done while attending the University of Illinois.