RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Zh. Vychisl. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sib. Zh. Vychisl. Mat., 2001, Volume 4, Number 1, Pages 85–106 (Mi sjvm387)  

A decomposition method for singularly perturbed parabolic convectiondiffusion equations with discontinuous initial conditions

G. I. Shishkin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Grid approximations of the Cauchy one-dimensional problem for singularly perturbed parabolic equations are considered. The limit equation (with $\varepsilon=0$, where $\varepsilon$ is the perturbation parameter multiplying the highest derivative) contains the derivative with respect to the spatial variable (convective term). The initial condition has a discontinuity of the first kind. The solution of this problem has singularities in a neighbourhood of the discontinuity for fixed values of the parameter $\varepsilon$, and also a transient layer for small values of $\varepsilon$. We construct special finite difference schemes which $\varepsilon$ uniformly converge on the whole domain. For this we use the domain and solution decomposition technique. The singular solution, generated by the discontinuity of the initial function, is split off and represented in the explicit form in the nearest neighbourhood of the discontinuity. In the neighbourhood of the transient layer, we employ the meshes condensing by a special way.

Full text: PDF file (1084 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 519.63
Received: 09.03.2000

Citation: G. I. Shishkin, “A decomposition method for singularly perturbed parabolic convectiondiffusion equations with discontinuous initial conditions”, Sib. Zh. Vychisl. Mat., 4:1 (2001), 85–106

Citation in format AMSBIB
\Bibitem{Shi01}
\by G.~I.~Shishkin
\paper A~decomposition method for singularly perturbed parabolic convectiondiffusion equations with discontinuous initial conditions
\jour Sib. Zh. Vychisl. Mat.
\yr 2001
\vol 4
\issue 1
\pages 85--106
\mathnet{http://mi.mathnet.ru/sjvm387}
\zmath{https://zbmath.org/?q=an:0969.65089}


Linking options:
  • http://mi.mathnet.ru/eng/sjvm387
  • http://mi.mathnet.ru/eng/sjvm/v4/i1/p85

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
    Number of views:
    This page:203
    Full text:54
    References:36

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020