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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the computation of solutions of boundary value problems on infinite intervals
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by R. M. M. Mattheij PDF
Math. Comp. 48 (1987), 533-549 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 48 (1987), 533-549
  • MSC: Primary 65L10
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0878689-4
  • MathSciNet review: 878689