Skip to main content
Log in

Aniterative method for the solution of some singularly perturbed cauchy problems

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We construct an iterative method for the solution of Cauchy problems for systems of singularly perturbed equations with fast time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Yu. P. Boglaev, “Iterative method for the approximate solution of singularly perturbed problems,” Dokl. Akad. Nauk SSSR, 227, No. 5, 1033–1036 (1976).

    MathSciNet  Google Scholar 

  2. M. G. Dmitriev, “Iterative solution of problems of optimal control with slow and fast motion,” Dokl. Akad Nauk SSSR, No. 2, 1145–1149 (1983).

    MathSciNet  Google Scholar 

  3. I. N. Shchitov, “Asymptotics of solutions of systems with slow and fast variables,”, Ukr. Mat. Zh., 39, No. 5, 631–637 (1987).

    MATH  MathSciNet  Google Scholar 

  4. N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

    MATH  Google Scholar 

  5. A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  6. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, Berlin (1975).

    MATH  Google Scholar 

Download references

Authors

Additional information

Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1055–1060, August, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mel'nik, T.A. Aniterative method for the solution of some singularly perturbed cauchy problems. Ukr Math J 49, 1183–1190 (1997). https://doi.org/10.1007/BF02487547

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487547

Keywords

Navigation