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Sukhanov’s Variable Initial Value Method for Boundary Value Problems

  • Harriet Kagiwada
  • Robert Kalaba
  • Nima Rasakhoo
  • Karl Spingarn
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 31)

Abstract

In 1983, Sukhanov presented a new method for transforming a nonlinear two-point boundary value problem into an initial value problem (Reference 1). Sukhanov’s approach involves only the solution of ordinary differential equations and not partial differential equations as in other initial value methods for nonlinear two-point boundary value problems (References 2, 3, and 8). In this chapter, Sukhanov’s method is applied to second order and fourth-order nonlinear two-point boundary value problems.

Keywords

Main Program Grid Interval Unknown Initial Condition Unknown Boundary Condition Initial Condition Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Chapter 5

  1. 1.
    sukhanov, A. A., A method of solution of nonlinear two-point boundary value problems, Journal of Numerical Mathematics and Mathematical Physics ,Vol. 23, pages 228–231, 1983 (in Russian).MathSciNetMATHGoogle Scholar
  2. 2.
    kalaba, R., and Spingarn, K., Control, Identification, and Input Optimization ,Plenum Press, New York, 1982.MATHGoogle Scholar
  3. 3.
    Bellman, R. E., and Kalaba, R., Quasilinearization and Nonlinear Boundary-Value Problems ,Elsevier, New York, 1965.MATHGoogle Scholar
  4. 4.
    Kagiwada, H., Kalaba, R., Rasakhoo, N., and Spingarn, K., Numerical experiments using Sukhanov’s initial-value method for nonlinear two-point boundary value problems, Computers and Mathematics with Applications ,Vol. 10, Nos. 4/5, pp. 327–330, 1984.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Kagiwada, H., Kalaba, R., Rasakhoo, N., and Spingarn, K., Numerical experiments using Sukhanov’s initial value method for nonlinear two-point boundary value problems II, Journal of Optimization Theory and Applications ,Vol. 46, No. 1, May 1985.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kagiwada, H., Kalaba, R., Rasakhoo, N., and pingarn, K., Numerical experiments using Sukhanov’s initial-value method for nonlinear two-point boundary value problems III, Nonlinear Analysis, Theory, Methods, and Applications ,Vol. 8, No. 12, pp. 1497–1505, December 1984.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Kagiwada, H., Kalaba, R., Rasakhoo, N., and Spingarn, K., Numerical experiments using Sukhanov’s initial-value method for nonlinear two-point boundary value problems IV, Nonlinear Analysis, Theory, Methods, and Applications ,Vol. 9, No. 5, pp. 469–477, 1985.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Kagiwada, H., and Kalaba, R., Derivation and validation of an initial-value method for certain nonlinear two-point boundary value problems, Journal of Optimization Theory and Applications ,Vol. 2, No. 6, pp. 378–385, 1968.MATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Harriet Kagiwada
    • 1
  • Robert Kalaba
    • 1
  • Nima Rasakhoo
    • 1
  • Karl Spingarn
    • 1
  1. 1.Hughes Aircraft CompanyEl SegundoUSA

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