The numerical solution of a challenging class of turning point problems

Ping Lin, R. E. O'Malley

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    A curious class of challenging singularly perturbed turning point problems is considered and properties of the solutions to corresponding initial value problems are studied. The solutions are exponentially small near the turning point and become unstable after passing it. Various state-of-the-art codes available in MATLAB as well as one-step and multistep methods on a uniform mesh are tested. By examining a number of examples, one finds that the usual error control strategies may not work when the solution near the turning point is small, while one-step and multistep methods on a uniform mesh work only for a moderately small perturbation parameter. A scale amplification transformation, however, seems to give the correct solution when the solution is extremely small and/or zero at the turning point. Extensions to problems with more equilibria are also briefly considered.
    Original languageEnglish
    Pages (from-to)927-941
    Number of pages15
    JournalSIAM Journal on Scientific Computing
    Volume25
    Issue number3
    DOIs
    Publication statusPublished - 2003

    Keywords

    • Singular perturbation
    • Turning points
    • ODE solvers
    • Runge-Kutta methods
    • Multistep methods

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