Skip to main content
SpringerLink
Log in

Exponential-fitting methods for the numerical integration of the fourth-order differential equation yIV+f·y=g

Exponentialanpassungsmethoden für die numerische Integration der Differentialgleichung yIV+f·y=g

  • Published:
Computing Aims and scope Submit manuscript

Abstract

A class of multistep methods is derived from the Chebyshevian multistep theory of Lyche for the numerical integration of the fourth-order differential equation of the formy IV+f·y=g. The new methods are significantly more accurate than the classical methods iff(x) is a nearly constant function.

Zusammenfassung

Für die numerische Integration der Differentialgleichungy IV+f·y=g wird mittels der Chebyshev-Multisteptheorie von Lyche eine Klasse von Mehrschrittverfahren hergeleitet. Die neuen Methoden sind bedetend genauer als die klassischen Methoden wennf(x) eine annähernd konstante Funktion ist.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Courant, R., Hilbert, D.: Methods of Mathematical Physics 1, p. 362, 395. New York: Interscience 1953.

    Google Scholar 

  2. Fox, L.: Numerical solution of two-point boundary value problems. Oxford University Press 1957.

  3. Gautschi, W.: Numerical integration of ordinary differential equations based on trigonometrical polynomials. Numer. Math.3, 381–387 (1961).

    Google Scholar 

  4. Henrici, P.: Discrete variable methods in ordinary differential equations, p. 164, 347., New York: J. Wiley 1962.

    Google Scholar 

  5. Jain, M. K., Iyengar, S. R. K., Saldanha, I. S. V.: Numerical solution of fourth-order ordinary differential equations. J. Eng. Math.11, 373–380 (1977).

    Google Scholar 

  6. Lambert, J. D., Watson, I. A.: Symmetric multistep methods for periodic initial value problems. J. Inst. Maths. Applic.18, 189–202 (1976).

    Google Scholar 

  7. Lyche, T.: Chebyshevian multistep methods for ordinary differential equations. Numer. Math.19, 65–74 (1972).

    Google Scholar 

  8. Raptis A., Allison, A. C.: Exponential-fitting methods for the numerical solution of the Schröndiger equation. Computer Phys. Commun.14, 1–5 (1978).

    Google Scholar 

  9. Timoshenko, S. P., Woinowsky-Kreger, S.: Theory of plates and shells, p. 30. New York: McGraw-Hill 1959.

    Google Scholar 

  10. Usmani, R. A., Marsden, M. J.: Numerical solution of some ordinary differential equations occuring in plate deflection theory. J. Engng. Math.9, 1–10 (1975).

    Google Scholar 

  11. Usmani, R. A.: An 0 (h 6) finite-difference analogue equations occurring in plate deflection theory. J. Inst. Math. Applic.20, 331–333 (1977).

    Google Scholar 

Download references

Author information

Author notes

  1. A. Raptis

    Present address: Chair of Numerical Analysis, National Technical University of Athens, 147, Athens, Greece

Authors and Affiliations

  1. Department of Mathematics and Statistics, City of London Polytechnic, London, UK

    A. Raptis

Authors
  1. A. Raptis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Raptis, A. Exponential-fitting methods for the numerical integration of the fourth-order differential equation yIV+f·y=g. Computing 24, 241–250 (1980). https://doi.org/10.1007/BF02281728

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02281728

Keywords

Search

Navigation