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TheA-stability of a family of fourth order methods

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Abstract

A proof is outlined showing that a fourth order exponentially fitted method isA-stable provided that the fitting parameterQ satisfiesQ≦z 06≈ −4.12779 wherez 06 is the negative root of the equation

$$\exp (Q)(2Q^4 + 3Q^3 - 18Q^2 + 72) + (Q^4 + 3Q^3 - 18Q^2 - 72Q - 72) = 0.$$

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References

  1. W. Enright, “Studies in the Numerical Solution of Stiff Ordinary Differential Equations”, Technical Report No. 46, Department of Computer Science, University of Toronto, 1972.

  2. L. W. Jackson and Surender Kumar Kenue,A Fourth Order A-stable Method, Technical Report TR 74-12, Department of Computing Science, University of Alberta, Edmonton, Alberta, 1974.

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  3. L. W. Jackson and Surender Kumar Kenue,A Fourth Order Exponentially Fitted Method, SIAM J. Num. Anal. 11 (1974), pp. 965–978.

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  4. L. W. Jackson,The Stability Analysis of a Fourth Order Exponentially Fitted Method, Technical Report TR 76-2, Department of Computing Science, University of Alberta, Edmonton, Alberta, 1976.

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  5. S. K. Kenue,Numerical Solution of Stiff Differential Equations, M. Sc. Thesis, University of Alberta, Edmonton, Alberta, 1972.

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  6. W. Liniger,Global Accuracy and A-stability of One and Two Step Integration Formulae for Stiff Ordinary Differential Equations inConference on the Numerical Solution of Differential Equations, Springer Verlag, Berlin, 1969, pp. 188–195.

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Authors and Affiliations

  1. Department Of Computing Science, University Of Alberta, Edmonton, Alberta

    L. W. Jackson

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  1. L. W. Jackson
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Jackson, L.W. TheA-stability of a family of fourth order methods. BIT 16, 383–387 (1976). https://doi.org/10.1007/BF01932721

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  • DOI: https://doi.org/10.1007/BF01932721

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