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BIT Numerical Mathematics

, Volume 23, Issue 3, pp 360–369 | Cite as

A class of hybrid formulae for the numerical integration of stiff systems

  • F. Patrício
Part II Numerical Mathematics

Abstract

A class of hybrid formulae suitable for the numerical integration of stiff systems of first order ordinary differential equations is presented. These formulae are defined in a predictor-corrector mode and contain an off-step pointxn+v, which is distinct from the points defined by the step used. The parameterv is examined in an attempt to obtain better stability properties and higher order formulae of one step only. We obtain order five and eitherA-stability or stiff-stability according to the values ofv used. Some numerical results are presented.

Keywords

Differential Equation Ordinary Differential Equation Computational Mathematic Good Stability Stability Property 
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References

  1. 1.
    J. R. Cash,Second derivative extended backward differentiation formulas for the numerical integration of stiff systems, Siam J. Num. An., 18 (1981), pp. 21–36.CrossRefGoogle Scholar
  2. 2.
    W. H. Enright,Second derivative multistep methods for stiff ordinary differential equations, Siam J. Num. An., 11 (1974), pp. 321–331.CrossRefGoogle Scholar
  3. 3.
    J. D. Lambert,Computational methods in ordinary differential equations, John Wiley and Sons, London (1973).Google Scholar
  4. 4.
    W. Liniger and R. A. Willoughby,Efficient numerical integration of stiff systems of ordinary differential equations, Technical Report RC-1970, IBM Thomas J. Watson Research Center, Yorktown Heights N.Y., (1967).Google Scholar

Copyright information

© BIT Foundations 1983

Authors and Affiliations

  • F. Patrício
    • 1
  1. 1.Departmento de MatemáticaUniversidade de CoimbraCoimbraPortugal

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