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Stability of a family of difference schemes for the Samarskii-Ionkin problem with variable coefficient

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Abstract

We consider a one-parameter family of difference schemes approximating a nonlocal heat problem with variable coefficient. We study the spectral properties of the main difference operator of the scheme. An energy norm in which the schemes are uniformly stable is defined on the space of grid functions. The corresponding stability condition is derived.

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References

  1. Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1989.

    Google Scholar 

  2. Ionkin, N.I., Difference Schemes for One Nonclassical Problem, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 1977, no. 2, pp. 20–32.

    Google Scholar 

  3. Gulin, A.V., Ionkin, N.I., and Morozova, V.A., Difference Schemes for Nonlocal Problems, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 1 (512), pp. 40–51.

    Google Scholar 

  4. Gulin, A.V., Ionkin, N.I., and Morozova, V.A., Investigation of the Norm in Problems of the Stability of Nonlocal Difference Schemes, Differ. Uravn., 2006, vol. 42, no. 7, pp. 914–923.

    MathSciNet  Google Scholar 

  5. Gulin, A.V., Ionkin, N.I., and Morozova, V.A., A Stability Criterion for a Difference Scheme for a Nonlocal Heat Problem, Izv. Vyssh. Uchebn. Zaved. Mat., 2007, no. 6 (541), pp. 21–28.

    Google Scholar 

  6. Gulin, A.V. and Mokin, A.Yu., Uniform Stability of a One-Parameter Family of Difference Schemes, Vestnik Moskov. Gos. Univ. Ser. XV Vychisl. Mat. Kibernet., 2011, no. 1, pp. 10–17.

    Google Scholar 

  7. Gulin, A.V., Morozova, V.A., and Udovichenko, N.S., Stability of a Nonlocal Difference Problem with a Complex Parameter, Differ. Uravn., 2011, vol. 47, no. 8, pp. 1105–1118.

    MathSciNet  Google Scholar 

  8. Ionkin, N.I. and Furletov, D.G., Uniform Convergence of a Family of Difference Schemes for a Nonclassical Boundary Value Problem with Variable Coefficients, Differ. Uravn., 1991, vol. 27, no. 7, pp. 1171–1177.

    MathSciNet  Google Scholar 

  9. Ionkin, N.I., Makarov, V.L., and Furletov, D.G., Stability and Convergence in the C-Norm of Difference Schemes for a Parabolic Equation with a Nonlocal Boundary Condition, Mat. Model., 1992, vol. 4, no. 4, pp. 63–73.

    MATH  MathSciNet  Google Scholar 

  10. Samarskii, A.A. and Gulin, A.V., Ustoichivost’ raznostnykh skhem (Stability of Difference Schemes), Moscow, 2005.

    Google Scholar 

  11. Mokin, A.Yu., On Spectral Properties of a Certain Nonself-Adjoint Difference Operator, Komput. Issled. Model., 2010, vol. 2, no. 2, pp. 143–150.

    Google Scholar 

  12. Il’in, V.A. and Poznyak, E.G., Osnovy matematicheskogo analiza (Foundations of Mathematical Analysis), Moscow, 2005, part I.

    Google Scholar 

  13. Il’in, V.A. and Kim, G.D., Lineinaya algebra i analiticheskaya geometriya (Linear Algebra and Analytic Geometry), Moscow, 2002.

    Google Scholar 

  14. Gulin, A.V., Ionkin, N.I., and Morozova, V.A., Ustoichivost’ nelokal’nykh raznostnykh skhem (Stability of Nonlocal Difference Schemes), Moscow, 2008.

    Google Scholar 

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  1. Moscow State University, Moscow, Russia

    A. Yu. Mokin

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  1. A. Yu. Mokin
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Correspondence to A. Yu. Mokin.

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Original Russian Text © A.Yu. Mokin, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 2, pp. 250–259.

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Mokin, A.Y. Stability of a family of difference schemes for the Samarskii-Ionkin problem with variable coefficient. Diff Equat 50, 254–263 (2014). https://doi.org/10.1134/S001226611402013X

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  • DOI: https://doi.org/10.1134/S001226611402013X

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