Multi-Adaptive Error Control for ODEs

Abstract

In this report we present a multi-adaptive continuous Galerkin method for the solution of initial value problems for ODEs. The method is multi-adaptive in the sense that the timesteps for the different components are chosen individually and adaptively, as based on an a posteriori estimate of the maximum global error.

It is also shown how the computation can be done in one sweep, with fixed and correct data for the dual problem and without having to iterate and alternate between the primal and the dual problems, and also without an excessive amount of work needed for the error control.