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Composite Multistep Methods and Stiff Stability

  • Theodore A. Bickart
  • William B. Rubin
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

A-stability [Dahlquist (1963A)] and its weaker associates, A[α]-stability [Widlund (1967A)] and stiff stability [Gear(1971D)],** have become generally accepted as appropriate properties of numerical methods suitable for solving a stiff initial value problem, as described by a first order vector ordinary differential equation
$$_{\dot X} \left( t \right) = f\left[ {_X \left( t \right),t} \right]$$
(1)
with initial condition
$$x\left( {t_0 } \right) = x_0 .$$
(2)

Keywords

Half Plane Characteristic Polynomial Stability Domain Open Disk Multistep Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1973 Rubin, W. B., “A-stability and composite multistep methods,” PhD Thesis, Syracuse University, New York.Google Scholar
  2. 1971 Bickart, T. A., Burgess, D. A., and Sloate, H. M., “High order A-stable composite multistep methods for numerical integration of stiff differential equations,” pp. 465-473 in Proc. Ninth Annual Allerton Conf. on Circuit and System Theory, University of Illinois.Google Scholar
  3. 1971 Sloate, H. M., “Simultaneous implicit formulas for the solution of stiff systems of differential equations,” PhD Thesis, Syracuse University, New York.Google Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • Theodore A. Bickart
    • 1
  • William B. Rubin
    • 2
  1. 1.Electrical and Computer Engineering DepartmentSyracuse UniversitySyracuseUSA
  2. 2.Poughkeepsie LaboratoryIBM CorporationPoughkeepsieUSA

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