Skip to main content
Log in

Application of the invariant embedding method for computing nonlinear periodic oscillations

  • Applied Topics in Control Theory, Mathematical Cybernetics, and Applied Statistics
  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The invariant embedding method is applied to compute periodic solutions of nonlinear systems that depend continuously on the perturbation frequency. Analysis of such systems in the region of multivalued solutions is demonstrated. An example of an essentially nonlinear system is examined.

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. L. I. Glukhivskii, "Numerical method for determination of periodic solutions of nonlinear differential equations by computer," Teor. Élektrotekh., No. 29, 159–164 (1980).

    Google Scholar 

  2. J. Casty and R. Calaba, Embedding Methods in Applied Mathematics [Russian translation], Moscow (1976).

  3. J. Lance, Numerical Methods for Fast Computers [in Russian], Moscow (1962).

  4. P. I. Monastyrnyi, "Toward a theory of the invariant embedding method for boundary-value problems," Dokl. Akad. Nauk BSSR,22, No. 4, 303–306 (1978).

    Google Scholar 

  5. T. Y. Na, Computational Methods in Engineering Boundary Value Problems, Academic Press, New York (1979).

    Google Scholar 

  6. R. V. Fil'ts, "A general method of mode calculations for nonlinear electrical-engineering systems," in: Converters in Thyristor Power Supplies [in Russian], Kishinev (1977), pp. 52–99.

  7. V. E. Shamanskii, Methods of Numerical Solution of Boundary-Value Problems by Computer [in Russian], part 2, Kiev (1966).

Download references

Authors

Additional information

Khar'kov Polytechnical Institute. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 136–140, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belomytsev, A.S., Karaban, V.N. Application of the invariant embedding method for computing nonlinear periodic oscillations. J Math Sci 69, 1476–1479 (1994). https://doi.org/10.1007/BF01250595

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01250595

Keywords

Navigation