Skip to main content
SpringerLink
Log in

Effective Application of the Fourier Technique for Constructing a Solution to a Mixed Problem for a Telegraph Equation

  • Published:
Moscow University Computational Mathematics and Cybernetics Aims and scope Submit manuscript

Abstract

An algorithm is presented for constructing and calculating a rapidly converging series that is a (generalized or classical) solution to a mixed problem for a telegraph equation considered in a half-strip. The case of an essentially non-self-adjoint operator with respect to the spatial variable is considered. The constructed series is a generalized d’Alembert formula. The proposed approach supersedes traditional variable separation for solving mixed problems, which usually results in slowly converging series.

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. V. A. Steklov, Fundamental Problems of Mathematical Physics (Nauka, Moscow, 1983) [in Russian].

    MATH  Google Scholar 

  2. A. N. Krylov, On Some Differential Equations of Mathematical Physics Having Applications in Engineering (GITTL, Leningrad, 1950) [in Russian].

    Google Scholar 

  3. V. A. Chernyatin, Substantiation of the Fourier Method in Mixed Problems for Partial Differential Equations (Mosk. Gos. Univ., Moscow, 1991) [in Russian].

    MATH  Google Scholar 

  4. M. Sh. Burlutskaya and A. P. Khromov, ‘‘Resolvent approach in the Fourier method,’’ Dokl. Math. 90 (2), 545–548 (2014).

    Article  MathSciNet  Google Scholar 

  5. A. P. Khromov, ‘‘On the convergence of the formal Fourier solution of the wave equation with a summable potential,’’ Comput. Math. Math. Phys. 56 (10), 1778–1792 (2016).

    Article  MathSciNet  Google Scholar 

  6. A. P. Khromov, ‘‘Necessary and sufficient conditions for the existence of a classical solution of the mixed problem for the homogeneous wave equation with an integrable potential,’’ Differ. Equations 55 (5), 703–717 (2019).

    Article  MathSciNet  Google Scholar 

  7. A. P. Khromov and V. V. Kornev, ‘‘Classical and generalized solutions of a mixed problem for a nonhomogeneous wave equation,’’ Comput. Math. Math. Phys. 59 (2), 275–289 (2019).

    Article  MathSciNet  Google Scholar 

  8. A. P. Khromov, ‘‘Divergent series and the Fourier method for the wave equation,’’ in Modern Problems of the Theory of Functions and Their Approximations: Proc. 20th Int. Saratov Winter School (Nauchnaya Kniga, Saratov, 2020), pp. 433–439 [in Russian].

  9. L. Euler, Differential Calculus (GITTL, Moscow–Leningrad, 1950) [in Russian].

    Google Scholar 

Download references

ACKNOWLEDGMENTS

The author is grateful to A.P. Khromov for his helpful comments of the results of this work.

Funding

This work was supported by the Moscow Center for Fundamental and Applied Mathematics.

Author information

Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    I. S. Lomov

Authors
  1. I. S. Lomov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. S. Lomov.

Additional information

Translated by I. Tselishcheva

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lomov, I.S. Effective Application of the Fourier Technique for Constructing a Solution to a Mixed Problem for a Telegraph Equation. MoscowUniv.Comput.Math.Cybern. 45, 168–173 (2021). https://doi.org/10.3103/S0278641921040038

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0278641921040038

Keywords:

Search

Navigation