Skip to main content
SpringerLink
Log in

Additive Schemes for Systems of Time-Dependent Equations of Mathematical Physics

  • Conference paper
  • First Online:
Book cover Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

Included in the following conference series:

Abstract

Additive difference schemes are derived via a representation of an operator of a time-dependent problem as a sum of operators with a more simple structure. In doing so, transition to a new time level is performed as a solution of a sequence of more simple problems. Such schemes in various variants are employed for approximate solving complicated time-dependent problems for PDEs. In the present work construction of additive schemes is carried out for systems of parabolic and hyperbolic equations of second order. As examples there are considered dynamic problems of the elasticity theory for materials with variable properties, dynamics problems for an incompressible fluid with a variable viscosity, general 3D problems of magnetic field diffusion.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Yanenko, N. N.: The Method of Fractional Steps. Springer-Verlag, New York (1967)

    Google Scholar 

  2. Samarskii, A. A.: The Theory of Difference Schemes. Marcell Dekker (2001)

    Google Scholar 

  3. Marchuk, G.I.: Splitting and alternating direction methods. In: Ciarlet, P. G., Lions, J.-L. (eds): Handbook of Numerical Analysis, Vol. 1. North-Holland, Amsterdam (1990) 197–462

    Chapter  Google Scholar 

  4. Samarskii, A. A., Vabishchevich, P. N.: Computational Heat Transfer, Vol.1,2. Wiley, Chichester (1995)

    Google Scholar 

  5. Samarskii, A. A., Vabishchevich, P. N.: Additive Schemes for Problems of Mathematical Physics. Nauka, Moscow (1999) (in Russian)

    Google Scholar 

  6. Samarskii, A. A., Vabishchevich, P. N., Matus, P. P.: Difference Schemes with Operator Factors. Minsk (1998) (in Russian)

    Google Scholar 

  7. Samarskii, A. A.: An economical algorithm for numerical solution of systems of differential and algebraic equations. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki. 4 (1964) 580–585 (in Russian)

    MathSciNet  Google Scholar 

  8. Peaceman, D. W., Rachford, H. H.: The numerical solution of parabolic and elliptic differential equations. J. SIAM. 3 (1955) 28–41

    MATH  MathSciNet  Google Scholar 

  9. Samarskii, A. A., Gulin, A. V.: Stability of Difference Schemes. Nauka, Moscow (1973) (in Russian)

    Google Scholar 

  10. Vabishchevich, P. N., Samarskii, A. A.: Solution of problems of incompressible fluid dynamics with variable viscosity. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki. 40 (2000) 1813–1822 (in Russian)

    MathSciNet  Google Scholar 

  11. Lisbona, F. L., Vabishchevich, P. N.: Operator-splitting schemes for solving elasticity problems. Comput. Methods in Applied Math. 1 (2001) 188–198

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RAS, Institute for Mathematical Modeling, 4-A Miusskaya Square, 125047, Moscow, Russia

    Alexander Samarskii & Petr Vabishchevich

Authors
  1. Alexander Samarskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petr Vabishchevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Samarskii, A., Vabishchevich, P. (2003). Additive Schemes for Systems of Time-Dependent Equations of Mathematical Physics. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-36487-0_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation