Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Nonlinear explicit difference schemes for solving parabolic equations

  • 40 Accesses

Abstract

A method is proposed for solving initial-boundary-value problems for parabolic equations by means of reducing them to Cauchy problems for systems of ordinary differential equations and applying to the latter nonlinear explicit numerical methods.

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

References

  1. 1.

    A. A. Bykov, “On numerical solution of stiff Cauchy problems for systems of linear ordinary differential equations,” Vychislitel'nye Metody i Programmirovanie, No. 38, 173–181 (1983).

  2. 2.

    Ya. N. Glinskii, “On a certain method of regularization of explicit Runge-Kutta schemes,” in: Numerical Methods for Solving Problems of Mathematical Physics, No. 3 [in Russian], Znanie, Moscow (1963).

  3. 3.

    Ya. N. Glinskii, “Explicit methods for solving stiff systems of ordinary differential equations,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 2, 74–78 (1981).

  4. 4.

    N. N. Kalitkin and I. V. Ritus, “A scheme with complex coefficients for solving parabolic equations,” Preprint No. 32, Akad. Nauk SSSR, Institute of Applied Mathematics, Moscow (1981).

  5. 5.

    Ya. N. Pelekh, “An explicit A-stable method of the fourth order of accuracy for numerical integration of differential equations,” Mat. Metody Fiz.-Mekh. Polya, No. 15, 19–23 (1982).

  6. 6.

    A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).

Download references

Author information

Additional information

Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 28–30, 1987.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Glinskii, Y.N. Nonlinear explicit difference schemes for solving parabolic equations. J Math Sci 65, 1943–1945 (1993). https://doi.org/10.1007/BF01097476

Download citation

Keywords

  • Differential Equation
  • Ordinary Differential Equation
  • Cauchy Problem
  • Difference Scheme
  • Parabolic Equation