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Derivation and validation of initial-value methods for boundary-value problems for difference equations

  • Michael A. Golberg
Contributed Papers

Abstract

In this paper, we develop the theory of invariant imbedding for general classes of two-point boundary-value problems for difference equations. In addition to deriving invariant imbedding equations, we show that the functions satisfying these equations in fact solve the original boundary-value problems.

Keywords

Difference Equation General Classis Invariant Imbed Imbed Equation Invariant Imbed Equation 
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References

  1. 1.
    Falb, P. L., andDeJong, J. L.,Some Successive Approximation Methods in Control and Oscillation Theory, Academic Press, New York, 1969.Google Scholar
  2. 2.
    Golberg, M. A.,Invariant Imbedding for a General Class of Boundary-Value Problems for Difference Equations (to appear).Google Scholar
  3. 3.
    Golberg, M. A.,A Generalized Invariant Imbedding Equation, III: Non-linear Boundary Conditions, Journal of Mathematical Analysis and Applications (to appear).Google Scholar
  4. 4.
    Kagiwada, H., andKalaba, R. E.,Verification of the Invariant Imbedding Method for Certain Fredholm Integral Equations, Journal of Mathematical Analysis and Applications, Vol. 23, No. 3, 1968.Google Scholar
  5. 5.
    Golberg, M. A.,Some Invariance Principles for Two-Point Boundary-Value Problems, Journal of Mathematical Analysis and Applications (to appear).Google Scholar

Additional Bibliography

  1. 6.
    Bailey, P. B., andWing, G. M.,Some Recent Developments in Invariant Imbedding with Applications, Journal of Mathematical Physics, Vol. 6, No. 3, 1965.Google Scholar
  2. 7.
    Bellman, R. E., Kalaba, R. E., andWing, G. M.,Invariant Imbedding and Neutron Transport Theory, III: Neutron-Neutron Collision Processes, Journal of Mathematics and Mechanics, Vol. 8, No. 2, 1959.Google Scholar
  3. 8.
    Bellman, R. E., andCooke, K.,Existence and Uniqueness Theorems in Invariant Imbedding, II: Convergence of a New Difference Algorithm, Journal of Mathematical Analysis and Applications, Vol. 12, No. 2, 1965.Google Scholar

Copyright information

© Plenum Publishing Corporation 1971

Authors and Affiliations

  • Michael A. Golberg
    • 1
  1. 1.Department of MathematicsUniversity of NevadaLas Vegas

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