Modified defect correction algorithms for ODEs. Part II: Stiff initial value problems

Abstract

As shown in part I of this paper and references therein, the classical method of Iterated Defect Correction (IDeC) can be modified in several nontrivial ways, extending the flexibility and range of applications of this approach. The essential point is an adequate definition of the defect, resulting in a significantly more robust convergence behavior of the IDeC iteration, in particular, for nonequidistant grids. The present part II is devoted to the efficient high-order integration of stiff initial value problems. By means of model problem investigation and systematic numerical experiments with a set of stiff test problems, our new versions of defect correction are systematically evaluated, and further algorithmic measures are proposed for the stiff case. The performance of the different variants under consideration is compared, and it is shown how strong coupling between non-stiff and stiff components can be successfully handled.