Remarks on Picard-Lindelöf iteration. (English) Zbl 0673.65037

The author discusses the Picard-Lindelöf iteration for systems of autonomous linear ordinary differential equations on finite intervals and its various numerical variants. The discussion presented assumes that the coupling terms are of moderate size compared with the low time scales in the problem. It is shown that the speed of convergence is quite independent of step size even for very large time steps. This makes it possible to design strategies in which the mesh gets gradually refined during the iteration in such a way that the iteration error stays essentially on the level of discretization error.
Reviewer: I.Dvořák


65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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