Multirate numerical integration of ordinary differential equations
V. Savcenco (Eindhoven University of Technology, Netherlands)
Numerous phenomena from different areas of science and technology are modelled by systems of ordinary differential equations (ODEs).
For the numerical solution of systems of ODEs there are many methods available. These methods use time steps that are varying in time, but are constant over the components. However, there are many problems of practical interest, where the temporal variations have different time scales for different sets of the components. To exploit these local time scale variations, one needs multirate methods that use different, local time steps over the components. In these methods big time steps are used for the slow components and small time steps are used for the fast ones.
We design, analyze and test multirate methods for the numerical solution of ODEs. We develop a self-adjusting multirate time stepping strategy, in which the step size for a particular system component is determined by the local temporal variation of this solution component, in contrast to the use of a single step size for the whole set of components as in the traditional methods. The partitioning into different levels of slow to fast components is performed automatically during the time integration.