Acta Numerica

Research Article

Numerical solution of highly oscillatory ordinary differential equations

Linda R. Petzolda1, Laurent O. Jaya2 and Jeng Yena3

a1 Department of Computer Science, University of Minnesota, 4-192 EE/CS Bldg, 200 Union Street S.E., Minneapolis, MN 55455-0159, USA E-mail: petzold@cs.umn.edu

a2 Department of Computer Science, University of Minnesota, 4-192 EE/CS Bldg, 200 Union Street S.E., Minneapolis, MN 55455-0159, USA E-mail: na.ljay@na-net.ornl.gov

a3 Army High Performance Computing Research Center, University of Minnesota, 1100 Washington Ave. S., Minneapolis, MN 55415, USA E-mail: yen@ahpcrc.umn.edu

One of the most difficult problems in the numerical solution of ordinary differential equations (ODEs) and in differential-algebraic equations (DAEs) is the development of methods for dealing with highly oscillatory systems. These types of systems arise, for example, in vehicle simulation when modelling the suspension system or tyres, in models for contact and impact, in flexible body simulation from vibrations in the structural model, in molecular dynamics, in orbital mechanics, and in circuit simulation. Standard numerical methods can require a huge number of time-steps to track the oscillations, and even with small stepsizes they can alter the dynamics, unless the method is chosen very carefully.