Skip to main content

Numerical Analysis

  • Chapter

Abstract

The most important principles of numerical analysis will be the subject of this chapter. The solution of practical problems usually requires the application of a professional numerical library of numerical methods, developed for computers. Some of them will be introduced at the end of Section 19.8.3. Special computer algebra systems such as Mathematica and Maple will be discussed with their numerical programs in Chapter 20, p. 953 and in Section 19.8.4, p. 946. Error propagation and computation errors will be examined in Section 19.8.2, p. 939.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

19. Numerical Analysis

  1. Brenner, S.C.; Scott, L.R.: The Mathematical Theory of Finite Element Methods. — Springer-Verlag 1994.

    Google Scholar 

  2. Chapra, S.C.; Canale, R.P.: Numerical Methods for Engineers. — McGraw Hill 1989.

    Google Scholar 

  3. Collatz, L.: Numerical Treatment of Differential Equations. — Springer-Verlag 1966.

    Google Scholar 

  4. Davis, P.J.; Rabinowitz, P: Methods of Numerical Integration. — Academic Press 1984.

    Google Scholar 

  5. De Boor, C.: A Practical Guide to Splines. — Springer-Verlag 1978.

    Google Scholar 

  6. Golub, G.; Ortega, J.M.: Scientific Computing. — B. G. Teubner 1996.

    Google Scholar 

  7. Grossmann, Ch.; Roos, H.-G.: Numerik partieller Differentialgleichungen. — B. G. Teubner 1992.

    Google Scholar 

  8. Hackbusch, W.: Elliptic Differential Equations. — Springer-Verlag 1992.

    Google Scholar 

  9. Hämmerlin, G.; Hoffmann, K.-H.: Numerische Mathematik. — Springer-Verlag 1994.

    Google Scholar 

  10. Hairer, E.; Norsett, S.P.; Wanner, G.: Solving Ordinary Differential Equations. Vol. 1: Nonstiff Problems. Vol. 2: Stiff and Differential Problems. Vol. 3: Algebraic Problems. — Springer-Verlag 1994.

    Google Scholar 

  11. Heitzinger, W.; Troch, I.; Valentin, G.: Praxis nichtlinearer Gleichungen. — C. Hanser Verlag 1984.

    Google Scholar 

  12. Kiełbasiński, A.; Schwetlick, H.: Numerische lineare Algebra. Eine computerorientierte Einführung. — Verlag H. Deutsch 1988.

    Google Scholar 

  13. Knothe, K.; Wessels, H.: Finite Elemente. Eine Einführung für Ingenieure. — Springer-Verlag 1992.

    Google Scholar 

  14. Kress, R.: Numerical Analysis. — Springer-Verlag 1998.

    Google Scholar 

  15. Lancaster, P.; Salkauska, S.K.: Curve and Surface Fitting. — Academic Press 1986.

    Google Scholar 

  16. Maess, G.: Vorlesungen über numerische Mathematik, Bd. 1, 2. — Akademie-Verlag 1984–1988.

    Google Scholar 

  17. Meinardus, G.: Approximation von Funktionen und ihre numerische Behandlung. — Springer-Verlag 1964.

    Google Scholar 

  18. NÜrnberger, G.: Approximation by Spline Functions. — Springer-Verlag 1989.

    Google Scholar 

  19. Pao, Y.-C: Engineering Analysis. — Springer-Verlag 1998.

    Google Scholar 

  20. Quarteroni, A.; Valli, A.: Numerical Approximation of Partial Differential Equations. — Springer-Verlag 1994.

    Google Scholar 

  21. Reinsch, Chr.: Smoothing by Spline Functions. — Numer. Math. 1967.

    Google Scholar 

  22. Schwarz, H.R.: Methode der finiten Elemente. — B. G. Teubner 1984.

    Google Scholar 

  23. Schwarz, H.R.: Numerische Mathematik. — B. G. Teubner 1986.

    Google Scholar 

  24. Schwetlick, H.; Kretzschmar, H.: Numerische Verfahren für Naturwissenschaftler und Ingenieure. — Fachbuchverlag 1991.

    Google Scholar 

  25. Stoer, J.; Bulirsch, R.: Introduction to Numerical Analysis. — Springer-Verlag 1993.

    Google Scholar 

  26. Stroud, A.H.: Approximate Calculation of Multiple Integrals. — Prentice Hall 1971.

    Google Scholar 

  27. TÖRNIG, W.: Numerische Mathematik für Ingenieure und Physiker, Bd. 1, 2. — Springer-Verlag 1990.

    Google Scholar 

  28. Überhuber, C: Numerical Computation 1, 2. — Springer-Verlag 1997.

    Google Scholar 

  29. Willers, F.A.: Methoden der praktischen Analysis. — Akademie-Verlag 1951.

    Google Scholar 

  30. Zurmühl, R.: Praktische Mathematik für Ingenieure und Physiker. — Springer-Verlag 1984.

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2007). Numerical Analysis. In: Handbook of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72122-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72122-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72121-5

  • Online ISBN: 978-3-540-72122-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics