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Mathematics of Computation

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On the computation of solutions of boundary value problems on infinite intervals

Author: R. M. M. Mattheij
Journal: Math. Comp. 48 (1987), 533-549
MSC: Primary 65L10
MathSciNet review: 878689
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Abstract: For solutions of linear boundary value problems defined on $[0,\infty )$ one has to study the stable or bounded solution manifold. A characterization of these manifolds is investigated here. A multiple shooting type algorithm is then developed to compute such solutions. This algorithm is fully adaptive and also covers problems where the ODE matrix does not tend to a limit (as is usually assumed), if the unstable manifold consists only of exponentially growing solutions. If the latter manifold also contains polynomially growing solutions, an extrapolation type approach is suggested. The theory is illustrated by a number of examples.

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Article copyright: © Copyright 1987 American Mathematical Society