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On optimal shooting intervals. (English) Zbl 0532.65054

In this interesting and well written paper, the authors consider in detail the issue of the optimal positioning of shooting points in a multiple shooting algorithm, for first order linear boundary value problems. A good mix of theoretical insight and reasonable heuristic is used to derive strategies for optimizing the shooting points position, with respect to computing time and stability. The resulting criterium is that of ”equidistributing the shooting points.” By this, it is meant that the shooting points should be chosen so that in each subinterval the number of mesh points used by the integrator is constant.

A number of suggestions are made to improve the efficiency of (any) multiple shooting code. Among the most important we mention: a) Use the adaptive mesh integrator only once, when computing the particular solution, and then use the same mesh for computing the fundamental solution: b) Do condensation of several shooting intervals into one to diminish storage requirements, but still preserving stability. A number of numerical examples illustrate the main points of the paper.

Reviewer: V.Pereyra
MSC:
65L10Boundary value problems for ODE (numerical methods)
65L50Mesh generation and refinement (ODE)
34B05Linear boundary value problems for ODE