Skip to main content

Part of the book series: Springer Series in Computational Physics ((SCIENTCOMP))

  • 2157 Accesses

Abstract

A broad conclusion from Chap. 7 is that implicit schemes are more effective than explicit schemes for problems with significant dissipation, as exemplified by the one-dimensional diffusion equation.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
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

  • Douglas, J., Gunn, J.E. (1964): Numer. Math. 6, 428–453

    Article  MathSciNet  MATH  Google Scholar 

  • Dwoyer, D., Thames, F. (1981): “Accuracy and Stability of the Time-Split Finite Difference Schemes”, AIAA Paper 81-1005.

    Google Scholar 

  • Fletcher, C.A.J. (1984): Computational Galerkin Methods, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    Google Scholar 

  • Fletcher, C.A.J., Srinivas, K. (1984): Comp. Meth. Appl. Mech. Eng. 46, 313–327

    Article  MATH  Google Scholar 

  • Gourlay, A.R. (1970): J. Inst. Math. Its Appl. 6, 375–390

    Article  MathSciNet  MATH  Google Scholar 

  • Gourlay, A.R. (1977): “Splitting Methods for Time Dependent Partial Differential Equations”, in The State of the Art in Numerical Analysis, ed. by D. Jacobs (Academic, London)

    Google Scholar 

  • Marchuk, G.I. (1974): Numerical Methods in Weather Prediction (Academic, New York)

    Google Scholar 

  • Mase, G.E. (1971): Continuum Mechanics (McGraw-Hill, New York)

    Google Scholar 

  • Mitchell, A.R., Fairweather, G. (1964): Numer. Math. 6, 285–292

    Article  MathSciNet  MATH  Google Scholar 

  • Mitchell, A.R., Griffiths, D.F. (1980): The Finite Difference Method in Partial Differential Equations (Wiley-Interscience, New York)

    MATH  Google Scholar 

  • Peaceman, D.W., Rachford, H.H. (1955): SIAM J. 3, 28–41

    MathSciNet  MATH  Google Scholar 

  • Yanenko, N. N. (1971): The Method of Fractional Steps, trans, by M. Holt (Springer; New York, Berlin, Heidelberg)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fletcher, C.A.J. (1998). Multidimensional Diffusion Equation. In: Computational Techniques for Fluid Dynamics 1. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58229-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-58229-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53058-9

  • Online ISBN: 978-3-642-58229-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics