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Backward differentiation formulas with extended regions of absolute stability

  • Part II Numerical Mathematics
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Abstract

This paper presents a class of (p + 2)-step backward differentiation formulas of orderp. The two extra degrees of freedom obtained by limiting the order of a (p + 2)-step formula top are used to extend the region of absolute stability. A new formula of orderp has a region of absolute stability very similar to that of a classical backward differentiation formula of orderp - 1 forp being in the range 4–6. The backward differentiation formulas with extended regions of absolute stability are constructed by appending two exponential-trigonometric terms to the polynomial basis of the classical formulas. Besides the absolute stability, the paper discusses relative stability and contractivity. The principles of an experimental implementation of the new formulas are outlined, and a linear problem integrated with this computer program indicates that the extended regions of absolute stability can actually be exploited in practice.

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Authors and Affiliations

  1. Danish Research Center for Applied Electronics, Venlighedsvej 4, DK-2970, Hørsholm, Denmark

    Stig Skelboe & Brian Christensen

  2. Risø National Laboratory, P.O. Box 49, DK-4000, Roskilde, Denmark

    Stig Skelboe & Brian Christensen

Authors
  1. Stig Skelboe
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  2. Brian Christensen
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Skelboe, S., Christensen, B. Backward differentiation formulas with extended regions of absolute stability. BIT 21, 221–231 (1981). https://doi.org/10.1007/BF01933167

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