Skip to main content
SpringerLink
Log in
Book cover

Numerical Methods in Fluid Dynamics pp 199–268Cite as

Telenin’s Method and the Method of Lines

  • Chapter

  • 285 Accesses

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

Abstract

The Method of Integral Relations, described in Chapt. 5, is one technique for reducing the amount of finite difference computation in the numerical solution of partial differential equations. The reduction is achieved by integrating the governing equations in one or more coordinate directions and representing unknowns in integrands by polynomials or trigonometrical expansions in the respective coordinates. We then solve ordinary or partial differential equations (of lower order) for the unknown coefficients in these expansions.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Chattot, J. J.: J. Fluid Mechanics 86, 161–177 (1978).

    Article  MATH  ADS  Google Scholar 

  • Chattot, J. J., Holt, M.: Proc. 3rd. Int. Conf. on Numerical Methods in Fluid Mechanics. Lecture Notes in Physics No. 19, p. 86–91. Berlin-Heidelberg-New York: Springer 1973.

    Book  Google Scholar 

  • Chushkin, P. I., Shchennikov, V. V.: Zh. Inzh. Fiz. Akad. Nauk SSSR 3, 88–94 (1962).

    Google Scholar 

  • Cuffel, R. F., Back, L. H., Massier, P. F.: AIAA J. 7, 1364–1366 (1969).

    Article  ADS  Google Scholar 

  • Emmons, H. W.: NACA TN 1003, 1946.

    Google Scholar 

  • Fletcher, C.A.J.: Proc. Fourth Int. Conf. on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics No. 35, p. 161–166. Berlin-Heidelberg-New York: Springer 1975a.

    Book  Google Scholar 

  • Fletcher, C.A. J.: AIAA J. 13, No. 8 (1975b).

    Google Scholar 

  • Friedman, M. P.: J. Aerospace Sci. 29, 4 (1962).

    Google Scholar 

  • Gilinskii, S. M., Telenin, G. F., Tinyakov, G. P.: Izv. Akad. Nauk, SSSR Mekh. Mash. 4, 9–28 (1964) (Translated as NASA TT F297).

    Google Scholar 

  • Gilinskii, S. M., Telenin, G. F.: Izv. Akad. Nauk SSSR Mekh. Mash. 5, 148–156 (1964).

    Google Scholar 

  • Gilinskii, S. M., Lebedev, M. G.: Izv. Akad. Nauk SSSR Mekh. 1 (1965).

    Google Scholar 

  • Goldstein, S., Ward, G. N.: Aero. Quart. 2, 39–84 (1950).

    MathSciNet  Google Scholar 

  • Gross, M. B., Holt, M.: Proc. Symposium Transsonicum II, Göttingen 1975. pp 369–375. Berlin-Heidelberg-New York: Springer 1976.

    Google Scholar 

  • Holt, M., Blackie, J.: Aero. Sci. 23, 931–956 (1956).

    MathSciNet  Google Scholar 

  • Holt, M., Ndefo, D. E.: J. Comp. Phys. 5, 463–486 (1970).

    Article  MATH  ADS  Google Scholar 

  • Hopkins, D. F., Hill, D. E.: AIAA J. 4, 1337–1343 (1966).

    Article  ADS  Google Scholar 

  • Jones, D. J.: Aero. Rep. LR-507 (NRC No. 10361), Nat. Res. Council, Canada, Ottawa 1968.

    Google Scholar 

  • Jones, D. J.: Tables of Inviscid Supersonic Flow About Circular Cones at Incidence γ = 1.4, AGARDograph 137 (1969).

    Google Scholar 

  • Jones, D. J., South, J. C., Klunker, E. B.: J. Comp. Phys. 9, 496–527 (1972).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Jones, D. J., South, J. C.: Application of the Method of Lines to the Solution of Elliptic Partial Differential Equations. National Research Council of Canada, National Aeronautical Establishment NRC No. 18021 (1979).

    Google Scholar 

  • Kliegel, J. R., Levine, J. N.: AIAA J. 7, 1375–1378 (1969).

    Article  ADS  Google Scholar 

  • Klopfer, G. H., Holt, M.: Proc. Symposium Transsonicum II, Göttingen 1975. pp 376–383. Berlin-Heidelberg-New York: Springer 1976.

    Google Scholar 

  • Klunker, E. B., South, J. C., jr., Davis, R. M.: NASA TR R-374, 1971.

    Google Scholar 

  • Kopal, Z.: M.I.T. Dept. Elec. Eng. Center of Analysis Tech. Report 4, 1949.

    Google Scholar 

  • Kutler, P., Lomax, H.: Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics No. 8 (Ed. M. Holt), p. 24–29. Berlin-Heidelberg-New York: Springer 1971.

    Google Scholar 

  • Li, Kon-ming, Holt, M.: J. Fluid Mech. 114, 399–418 (1982).

    Article  MATH  ADS  Google Scholar 

  • Liskovets, O.A.: The Method of Lines (Review). Differentsial’nye Uravneniya 1, 1662–1678 (1965).

    Google Scholar 

  • Meng, J. C. S.: J. Comp. Phys. 15, 320–344 (1974).

    Article  MATH  ADS  Google Scholar 

  • Melnik, R. E.: AIAA J. 5, 631–637 (1967).

    Article  MATH  ADS  Google Scholar 

  • Ndefo, D. E.: Univ. of Calif., Berkeley, Aero. Sci. Rept. AS-68–2, 1968.

    Google Scholar 

  • Petrovskii, I. G.: Lectures on Partial Differential Equations. New York: Interscience 1964.

    Google Scholar 

  • Pirumov, U. G.: Izv. Akad. Nauk SSSR Mekh. Zh. i G. 2, 10–22 (1967).

    Google Scholar 

  • Powell, M. J. D.: Computer J. 7, 303–307 (1964).

    Article  Google Scholar 

  • Stone, A. H.: J. Math. Phys. 27, 67–81 (1948a).

    MATH  Google Scholar 

  • Stone, A. H.: J. Math. Phys. 30, 200–213 (1948b).

    Google Scholar 

  • Tinyakov, G. P.: Izv. Akad. Nauk SSSR Mekh. No. 6, 10–19 (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Engineering, Mechanical Engineering, University of California, 94720, Berkeley, CA, USA

    Maurice Holt (Professor of Aeronautical Sciences)

Authors
  1. Maurice Holt
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin, Heidelberg

About this chapter

Cite this chapter

Holt, M. (1984). Telenin’s Method and the Method of Lines. In: Numerical Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69341-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-69341-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12799-4

  • Online ISBN: 978-3-642-69341-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation