Solution of a Nonlinear Heat Conduction Equation for a Curvilinear Region with Dirichlet Conditions by the Fast-Expansion Method

  • A. D. Chernyshov

The analytical solution of the nonlinear heat conduction problem for a curvilinear region is obtained with the use of the fast-expansion method together with the method of extension of boundaries and pointwise technique of computing Fourier coefficients.


nonlinear heat conduction equation curvilinear region fast-expansion method analytical solution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. M. Belyaev and A. A. Ryadno, Methods of Nonstationary Heat Conduction [in Russian], Vysshaya Shkola, Moscow (1978).zbMATHGoogle Scholar
  2. 2.
    É. M. Kartashov, Analytical Methods in the Theory of Thermal Conductivity of Solid Bodies [in Russian], Vysshaya Shkola, Moscow (2001).Google Scholar
  3. 3.
    S. P. Rudobashta, Calculation of the kinetics of drying disperse materials on the basis of analytical methods, J. Eng. Phys. Thermophys., 83, No. 4, 753–763 (2010).CrossRefGoogle Scholar
  4. 4.
    É. M. Kartashov, New integral relations for analytical solutions of parabolic-type equations in noncylindrical domains, J. Eng. Phys. Thermophys., 83, No. 4, 688–706 (2010).CrossRefGoogle Scholar
  5. 5.
    M. D. Kovalenko and T. D. Shulyakovskaya, Expansions in Fadle–Papkovich functions in the band. Foundations of the theory, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tel, No. 5. 78–98 (2011).Google Scholar
  6. 6.
    A. D. Chernyshov, Method of fast expansions for solving nonlinear differential equations, Zh. Vychisl. Mat. Mat. Fiz., 54, No. 1, 13–24 (2014).MathSciNetzbMATHGoogle Scholar
  7. 7.
    N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel′kov, Numerical Methods [in Russian], Nauka, Moscow (1987).Google Scholar
  8. 8.
    N. S. Piskunov, Differential and Integral Calculus [in Russian], Izd. Fiz.-Mat. Lit., Moscow (1985).zbMATHGoogle Scholar
  9. 9.
    A. D. Chernyshov, Method of extension of boundaries for the problems of heat conduction in bodies of mobile shape, J. Eng. Phys. Thermophys., 83, No. 5, 1054–1060 (2010).CrossRefGoogle Scholar
  10. 10.
    A. D. Chernyshov, Fast expansion operator and theorem of the singularity of fast expansions, in: Proc. Int. Conf. "Urgent Problems of Applied Mathematics, Informatics, and Mechanics," 26–28 November, 2012, Voronezhsk. Gos. Univ. Inzh. Tekhn., Voronezh (2012), Part 1, pp. 401–405.Google Scholar
  11. 11.
    A. D. Chernyshov and V. V. Goryainov, Application of the method of fast expansions for calculating the trajectories of a spaceship, Izv. Vyssh. Ucheb. Zaved., Aviats. Tekh., No. 2, 41–47 (2015).Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Voronezh State University of Engineering TechnologiesVoronezhRussia

Personalised recommendations