A double shooting scheme for certain unstable and singular boundary value problems
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- by Alvin Bayliss PDF
- Math. Comp. 32 (1978), 61-71 Request permission
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
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A. BAYLISS, Almost Periodic Solutions to Difference Equations, Courant Institute Report, IMM 409, 1975.
- C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0315898
- Herbert B. Keller, Numerical solution of two point boundary value problems, Regional Conference Series in Applied Mathematics, No. 24, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1976. MR 0433897
- 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
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 61-71
- MSC: Primary 65L10
- DOI: https://doi.org/10.1090/S0025-5718-1978-0464598-6
- MathSciNet review: 0464598