Skip to main content
SpringerLink
Log in

One-step multiderivative methods for first order ordinary differential equations

  • Part II Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed. The methods are extrapolated and analysed for use inPECE mode.

Error constants, stability intervals and stability regions are given in two associated Technical Reports.

Comparisons are made with well-known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors.

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. O. Axelsson,A class of A-stable methods, BIT 9 (1969), 185–199.

    Google Scholar 

  2. B. L. Ehle,High order A-stable methods for the numerical solution of systems of differential equations, BIT 8 (1968), 276–278.

    Google Scholar 

  3. A. R. Gourlay and J. Ll. Morris,The extrapolation of first order methods for parabolic partial differential equations II, SIAM J. Numer. Anal. 17(5) (1980), 641–655.

    Article  Google Scholar 

  4. J. D. Lambert,Computational Methods in Ordinary Differential Equations, Wiley, Chichester, 1973.

    Google Scholar 

  5. J. D. Lambert and A. R. Mitchell,On the solution of y′=f(x,y) by a class of high accuracy difference formulae of low order, Z. Angew. Math. Phys. 13 (1962), 223–232.

    Article  Google Scholar 

  6. J. D. Lawson and B. L. Ehle,Asymptotic error estimation for one-step methods based on quadrature, Aeq. Math. 5 (1970), 236–246.

    Article  Google Scholar 

  7. J. D. Lawson and J. Ll. Morris,The extrapolation of first order methods for parabolic partial differential equations I, SIAM J. Numer. Anal. 15(6) (1978), 1212–1224.

    Article  Google Scholar 

  8. B. Lindberg,On smoothing and extrapolation for the trapezoidal rule, BIT 11 (1971), 29–52.

    Google Scholar 

  9. W. E. Milne,A note on the numerical integration of differential equations, J. Res. Nat. Bur. Standards 43 (1949), 537–542.

    Google Scholar 

  10. M. H. Padé,Sur la répresentation approchée d'une fonction par des fractions rationelles, Ann. de l'École Normale Supérieure, Vol. 9 (Suppl.), 1892.

  11. E. H. Twizell and A. Q. M. Khaliq,One step multiderivative methods for first order ordinary differential equations, Brunel University Department of Mathematics Technical Report TR/02/81, 1981.

  12. E. H. Twizell and A. Q. M. Khaliq,Stability regions for one step multiderivative methods, Brunel University Department of Mathematics, Technical Report TR/04/81, 1981.

  13. E. H. Twizell and P. Smith,Numerical modelling of heat flow in the human torso I: finite difference methods, Proceedings of POLYMODEL4: diffusion convection problems, Sunderland Polytechnic, May 1981.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Brunel University, UB8 3PH, Uxbridge, Middlesex, England

    E. H. Twizell & A. Q. M. Khaliq

Authors
  1. E. H. Twizell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Q. M. Khaliq
    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

Twizell, E.H., Khaliq, A.Q.M. One-step multiderivative methods for first order ordinary differential equations. BIT 21, 518–527 (1981). https://doi.org/10.1007/BF01932848

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01932848

Keywords

Search

Navigation