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Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 804–807 | Cite as

A Method of Matching of Interior and Exterior Asymptotics in Boundary-Value Problems of Mathematical Physics

  • A. V. Shatrov
Article
  • 19 Downloads

Abstract

We describe applications of asymptotic methods to problems of mathematical physics and mechanics, primarily, to the solution of nonlinear singularly perturbed problems in local domains. We also discuss applications of Padé approximations for transformation of asymptotic expansions to rational or quasi-fractional functions.

Keywords and phrases

asymptotic methods Padé approximation boundary-value problem of mathematical physics boundary layer 

AMS Subject Classification

35Q35 41A21 

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References

  1. 1.
    E. A. Alekseeva, R. G. Barantsev, and A. V. Shatrov, “Matching of thermal asymptotics in a boundary layer,” Vestn. S.-Petersburg. Univ. Ser. 1, 8, 96–99 (1996).Google Scholar
  2. 2.
    I. V. Andrianov, “Application of Padé approximants in perturbation methods,” Adv. Mech., 14, No. 2, 3–15 (1991).MathSciNetGoogle Scholar
  3. 3.
    I. V. Andrianov, Yu. V. Mikhlin, and S. Tokarzhewsky, “Two-point Padé approximants and their applications to solving mechanical problems,” J. Theor. Appl. Mech., 35, No. 3, 577–606 (1997).zbMATHGoogle Scholar
  4. 4.
    G. A. Baker, G. A. Baker Jr., T. L. Gammel, “The Padé approximants,” J. Math. Anal. Appl., 2, No. 1, 21 (1961).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    R. G. Barantsev, “Definition of asymptotics and system triades,” in: Asymptotic Methods in the Theory of Systems [in Russian], Irkutsk (1980), pp. 70–81.Google Scholar
  6. 6.
    R. G. Barantsev and D. A. Pashkevich, “Matching of asymptotics in transition layers,” in: Asymptotic Methods in Problems of Aerodynamics and Design of Aircrafts [in Russian], Irkutsk (1994), pp. 67–70.Google Scholar
  7. 7.
    R. G. Barantsev, D. A. Pashkevich, and A. V. Shatrov, “Heat transfer in a boundary layer of reactive gas,” in: Heat/Mass Transfer MIF-2000 [in Russian], (2000), pp. 185–188.Google Scholar
  8. 8.
    M. D. Kruskal, “Asymptotology,” in: Mathematical Models in Physical Sciences (S. Drobot and P. A. Viebrock, eds.), Prentice-Hall, Englewood Cliffs, New Jersey (1963), pp. 17–48.Google Scholar
  9. 9.
    P. Martin and G. A. Baker Jr., “Two-point quasi-fractional approximant in physics. Truncation error,” J. Math. Phys., 32, No. 6, 1476–1477 (1991).CrossRefGoogle Scholar
  10. 10.
    A. V. Shatrov, “Combination of asymptotics in boundary-value problems of hydrodynamics,” in: Proc. Int. Conf. OFEA2001, June 25–29, 2001, St. Petersburg (2001), pp. 59–60.Google Scholar
  11. 11.
    A. V. Shatrov, “Matching of interior and exterior asymptotics in transition layers of viscous liquids and gases,” in: Proc. VIII All-Russian Conf. on Theor. and Appl. Mechanics, Perm’, August 23–29, 2001, Ural Branch RAS, Yekateringburg, (2001), pp. 602–603.Google Scholar
  12. 12.
    M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York–London (1964).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vyatka State UniversityKirovRussia

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