The application of invariant imbedding to the solution of linear two-point boundary value problems on an infinite interval

Author:
Dale W. Alspaugh

Journal:
Math. Comp. **28** (1974), 1005-1015

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1974-0351091-0

MathSciNet review:
0351091

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Abstract: Linear two-point boundary value problems defined on an infinite domain are converted to initial-value problems using invariant imbedding. The resulting Riccati equations are integrated numerically until the desired accuracy is obtained. Several criteria for determining the appropriate length of integration are presented. Several example problems are presented.

**[1]**T. N. Robertson,*The linear two-point boundary-value problem on an infinite interval*, Math. Comp.**25**(1971), 475–481. MR**0303742**, https://doi.org/10.1090/S0025-5718-1971-0303742-1**[2]**D. Alspaugh, H. Kagiwada, and R. Kalaba,*Dynamic programming, invariant imbedding and thin beam theory*, Internat. J. Engrg. Sci.**7**(1969), 1117–1126 (English, with French, German, Italian and Russian summaries). MR**0249018**, https://doi.org/10.1016/0020-7225(69)90079-2**[3]**D. W. Alspaugh, H. H. Kagiwada, and R. Kalaba,*Application of invariant imbedding to the buckling of columns*, J. Computational Phys.**5**(1970), 56–69. MR**0251952****[4]**D. W. ALSPAUGH & R. KALABA,*Direct Derivation of Invariant Imbedding Equations for Beams from a Variational Principle*, RAND Corp., RM-5995-PR, March 1969.**[5]**Paul B. Bailey and G. Milton Wing,*Some recent developments in invariant imbedding with applications*, J. Mathematical Phys.**6**(1965), 453–462. MR**0172663**, https://doi.org/10.1063/1.1704294**[6]**John Casti and Robert Kalaba,*Imbedding methods in applied mathematics*, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1973. Applied Mathematics and Computation, No. 2. MR**0471248****[7]**Gunter H. Meyer,*Initial value methods for boundary value problems*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Theory and application of invariant imbedding; Mathematics in Science and Engineering, Vol. 100. MR**0488791**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0351091-0

Keywords:
Boundary value problems,
invariant imbedding,
infinite domain

Article copyright:
© Copyright 1974
American Mathematical Society