Skip to main content

First order hyperbolic equations

  • 591 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 434)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Ansorge, C. Geiger and R. Hass, Existenz und numerische Erfassbarkeit verallgemeinerter Lösungen halblinearer Anfangswertaufgaben, Z. Angew. Math. Mech. 52 (1972), 597–605.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Ph. Brenner, The Cauchy problem for symmetric hyperbolic systems in Lp, Math. Scand. 19 (1966), 27–37.

    MathSciNet  MATH  Google Scholar 

  3. Ph. Brenner, The Cauchy problem for systems in Lp and Lp,α, Ark. Mat. 11 (1973), 75–101.

    CrossRef  MathSciNet  Google Scholar 

  4. Ph. Brenner and V. Thomée, Stability and convergence rates in Lp for certain difference schemes, Math. Scand. 27 (1970), 5–23.

    MathSciNet  MATH  Google Scholar 

  5. Ph. Brenner and V. Thomée, Estimates near discontinuities for some difference schemes. Math. Scand. 28 (1971), 329–340.

    MathSciNet  MATH  Google Scholar 

  6. G.W. Hedstrom, Norms of powers of absolutely convergent Fourier series, Michigan Math. J. 13 (1966), 393–416.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. G.W. Hedstrom, The rate of convergence of some difference schemes, SIAM J. Numer. Anal. 5 (1968), 363–406.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. V. Thomée, On maximum-norm stable difference operators, Numerical Solution of Partial Differential Equations, Ed. J.H. Bramble, Academic Press, New York 1966, 125–151.

    Google Scholar 

  9. V. Thomée, On the rate of convergence of difference schemes for hyperbolic equations, Numerical Solution of Partial Differential Equations II, Ed. B. Hubbard, Academic Press, New York 1971, 585–622.

    Google Scholar 

  10. V. Thomée, Convergence analysis of a finite difference scheme for a simple semi-linear hyperbolic equation, Numerische Behandlung nichtlinearer Integro-differential-and Differentialgleichungen, Springer Lecture Notes in Mathematics 395, 149–166.

    Google Scholar 

  11. L. Wahlbin, Maximum norm estimates for Friedrichs' scheme in two dimensions, to appear in SIAM J. Numer. Anal. 11 (1974).

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this chapter

Cite this chapter

Brenner, P., Thomée, V., Wahlbin, L.B. (1975). First order hyperbolic equations. In: Besov Spaces and Applications to Difference Methods for Initial Value Problems. Lecture Notes in Mathematics, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068130

Download citation

  • DOI: https://doi.org/10.1007/BFb0068130

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07130-3

  • Online ISBN: 978-3-540-37400-8

  • eBook Packages: Springer Book Archive