Skip to main content
SpringerLink
Log in

On an optimal method for solving an inverse Stefan problem

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

An algorithm optimal in order is proposed for solving an inverse Stefan problem. We also give some exact estimates of accuracy of this method.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. L. Gol’dman, Inverse Stefan Problems: Theory and Solution Methods (MGU, Moscow, 1999) [in Russian].

    Google Scholar 

  2. A. Friedman, Partial Differential Equations of Parabolic Type (Prentice-Hall, Englewood Cliffs, N.J., 1964; Mir, Moscow, 1968).

    MATH  Google Scholar 

  3. O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Optimal Methods for Solving the Ill-Posed Problems (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  4. M. M. Lavrent’ev and L. Ya. Savel’ev, Theory of Operators and Ill-Posed Problems (Sobolev Inst. Mat., Novosibirsk, 1999) [in Russian].

    MATH  Google Scholar 

  5. V. P. Tanana, “On Optimality by Order of the Method of Projective Regularization for Solving Inverse Problems,” Sibirsk. Zh. Industr. Mat. 7(2), 117–132 (2004).

    MATH  MathSciNet  Google Scholar 

  6. V. A. Ditkin and A. P. Prudnikov, Integral Transformations and Operational Calculus (Nauka, Moscow, 1961) [in Russian].

    Google Scholar 

  7. L. D. Menikhes and V. P. Tanana, “Finite-Dimensional Approximation in the M. M. Lavrent’ev Method,” Sibirsk. Zh. Vychisl. Mat. 1(1), 59–66 (1998).

    MathSciNet  Google Scholar 

  8. V. K. Ivanov and T. I. Korolyuk, “On an Error Estimate for Solution of Linear Ill-Posed Problems,” Zh. Vychisl. Mat. i Mat. Fiz. 9(1), 30–41 (1969).

    MATH  Google Scholar 

  9. V. N. Strakhov, “Solution of Linear Ill-Posed Problems in Hilbert Space,” Differentsial’nye Uravneniya 6(8), 1490–1495 (1970).

    MATH  Google Scholar 

  10. V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Ill-Posed Linear Problems and Its Applications (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

  11. V. P. Tanana, “On a New Approach to the Error Estimate of the Methods for Solving Ill-Posed Problems,” Sibirsk. Zh. Industr. Mat. 5(4), 150–163 (2002).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chelyabinsk State University, ul. Brat’ev Kashirinykh 129, Chelyabinsk, 454021, Russia

    V. P. Tanana & E. V. Khudyshkina

Authors
  1. V. P. Tanana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Khudyshkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.P. Tanana, E.V. Khudyshkina, 2005, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2005, Vol. VIII, No. 4(24), pp. 124–130.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tanana, V.P., Khudyshkina, E.V. On an optimal method for solving an inverse Stefan problem. J. Appl. Ind. Math. 1, 254–259 (2007). https://doi.org/10.1134/S1990478907020159

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478907020159

Keywords

Search

Navigation