Publications in Scientific Journals:
W. Auzinger, H. Hofstätter, W. Kreuzer, E. Weinmüller:
"Modified defect correction algorithms for ODEs. Part II: Stiff initial value problems";
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 and applications of this type of iterative schemes. The essential point is an adequate definition of the defect, leading to 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 experiment with a set of stiff test problems featuring different degrees of difficulty, 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.
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