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A double shooting scheme for certain unstable and singular boundary value problems


Author: Alvin Bayliss
Journal: Math. Comp. 32 (1978), 61-71
MSC: Primary 65L10
DOI: https://doi.org/10.1090/S0025-5718-1978-0464598-6
MathSciNet review: 0464598
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Abstract: A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.


References [Enhancements On Off] (What's this?)

  • [1] A. BAYLISS, Almost Periodic Solutions to Difference Equations, Courant Institute Report, IMM 409, 1975.
  • [2] C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0315898
  • [3] Herbert B. Keller, Numerical solution of two point boundary value problems, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1976. Regional Conference Series in Applied Mathematics, No. 24. MR 0433897
  • [4] José Luis Massera and Juan Jorge Schäffer, Linear differential equations and function spaces, Pure and Applied Mathematics, Vol. 21, Academic Press, New York-London, 1966. MR 0212324

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0464598-6
Article copyright: © Copyright 1978 American Mathematical Society