On the complete solution of ∈y″=y3 View Full Text


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Article Info

DATE

1994-02

AUTHORS

P. N. Müller, K. -D. Reinsch, R. Bulirsch

ABSTRACT

In Ref. 1, the author claimed that the problem ∈y″=y3 is soluble only for a certain range of the parameter ∈. An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of ∈. The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit ∈→0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small ∈ is obtained using a three-variable approach. More... »

PAGES

367-372

References to SciGraph publications

  • 1986-09. On the solution of εy″=y3 in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1965-02. Numerical calculation of elliptic integrals and elliptic functions in NUMERISCHE MATHEMATIK
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02192942

    DOI

    http://dx.doi.org/10.1007/bf02192942

    DIMENSIONS

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