# Sukhanov’s Variable Initial Value Method for Boundary Value Problems

• 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.

## 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&#x2013;231, 1983 (in Russian).
2. 2.
kalaba, R., and Spingarn, K., Control, Identification, and Input Optimization ,Plenum Press, New York, 1982.
3. 3.
Bellman, R. E., and Kalaba, R., Quasilinearization and Nonlinear Boundary-Value Problems ,Elsevier, New York, 1965.
4. 4.
Kagiwada, H., Kalaba, R., Rasakhoo, N., and Spingarn, K., Numerical experiments using Sukhanov&#x2019;s initial-value method for nonlinear two-point boundary value problems, Computers and Mathematics with Applications ,Vol. 10, Nos. 4/5, pp. 327&#x2013;330, 1984.
5. 5.
Kagiwada, H., Kalaba, R., Rasakhoo, N., and Spingarn, K., Numerical experiments using Sukhanov&#x2019;s initial value method for nonlinear two-point boundary value problems II, Journal of Optimization Theory and Applications ,Vol. 46, No. 1, May 1985.
6. 6.
Kagiwada, H., Kalaba, R., Rasakhoo, N., and pingarn, K., Numerical experiments using Sukhanov&#x2019;s initial-value method for nonlinear two-point boundary value problems III, Nonlinear Analysis, Theory, Methods, and Applications ,Vol. 8, No. 12, pp. 1497&#x2013;1505, December 1984.
7. 7.
Kagiwada, H., Kalaba, R., Rasakhoo, N., and Spingarn, K., Numerical experiments using Sukhanov&#x2019;s initial-value method for nonlinear two-point boundary value problems IV, Nonlinear Analysis, Theory, Methods, and Applications ,Vol. 9, No. 5, pp. 469&#x2013;477, 1985.
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&#x2013;385, 1968.

© Plenum Press, New York 1986