Numerische Mathematik

, Volume 10, Issue 2, pp 110–116 | Cite as

Monte Carlo path-integral calculations for two-point boundary-value problems

  • Takao Tsuda
  • Kozo Ichida
  • Takeshi Kiyono
Article

Abstract

A computational technique based on the method of path integral is studied with a view to finding approximate solutions of a class of two-point boundary-value problems. These solutions are “rough” solutions by Monte Carlo sampling. From the computational point of view, however, once these rough solutions are obtained for any nonlinear cases, they serve as good starting approximations for improving the solutions to higher accuracy. Numerical results of a few examples are also shown.

Keywords

Approximate Solution Mathematical Method Computational Technique Monte Carlo Sampling Computational Point 

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References

  1. [1]
    Milne, W. E.: Numerical solution of differential equations, Chapt. 7. New York: John Wiley & Sons 1953.Google Scholar
  2. [2]
    Holt, J. F.: Numerical solution of nonlinear two-point boundary problems by finite difference method. Comm. ACM7, 366–373 (1964).CrossRefGoogle Scholar
  3. [3]
    Clenshaw, C. W., andH. J. Norton: The solution of nonlinear ordinary differential equations in Chebyshev series. Comput. J.6, 88–92 (1963).CrossRefGoogle Scholar
  4. [4]
    Kac, M.: Lectures in applied mathematics, vol. 1. Proceedings of the Summer Seminar, Colorado 1957. New York: Interscience Publ. Inc. 1958.Google Scholar
  5. [5]
    Fosdick, L. D.: Approximation of a class of Wiener integrals. Math. Comput.19, 225–233 (1965).Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • Takao Tsuda
  • Kozo Ichida
  • Takeshi Kiyono
    • 1
  1. 1.Department of ElectronicsKyoto UniversityKyotoJapan

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