Numerical Algorithms

, Volume 20, Issue 2–3, pp 241–268 | Cite as

ODE-IVP-PACK via Sinc indefinite integration and Newton's method

  • F. Stenger
  • S.‐Å. Gustafson
  • B. Keyes
  • M. O'Reilly
  • K. Parker


This paper describes a package of computer programs for the unified treatment of initial-value problems for systems of ordinary differential equations. The programs implement a numerical method which is efficient for a general class of differential equations. The user may determine the solutions over finite or infinite intervals. The solutions may have singularities at the end-points of the interval for which the solution is sought. Besides giving the initial values and the analytical expression for the differential equations to be solved the user needs to specify the nature of the singularities and give some other analytical information as described in the paper in order to take advantage of the speed and accuracy of the package described here.

Sinc functions Sinc-points systems of ODE FORTRAN 65L05 34-04 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods (Wiley, New York, 1987).Google Scholar
  2. [2]
    W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math. 3 (1961) 381–397.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    C.W. Gear, Numerical Initial-Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, NJ, 1971).Google Scholar
  4. [4]
    S. Haber, Two formulas for numerical indefinite integration, Math. Comp., to appear.Google Scholar
  5. [5]
    R.B. Kearfott, A Sinc approximation for the indefinite integral, Math. Comp. 41 (1983) 559–572.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    J.D. Lambert, Numerical Methods for Ordinary Differential Systems: The Initial-Value Problem (Wiley, New York, 1991).Google Scholar
  7. [7]
    L.F. Shampine and M.K. Gordon, Computer Solution of Ordinary Differential Equations: The Initial-Value Problem (Freeman, San Francisco, 1975).Google Scholar
  8. [8]
    F. Stenger, Numerical methods based on the Whittaker cardinal, or Sinc functions, SIAM Rev. 23 (1981) 165–224.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    F. Stenger, Numerical Methods Based on Sinc and Analytic Functions (Springer, New York, 1993).Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • F. Stenger
  • S.‐Å. Gustafson
  • B. Keyes
  • M. O'Reilly
  • K. Parker

There are no affiliations available

Personalised recommendations