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A method of skipping the transient phase in the solution of separably stiff ordinary initial value problems


Author: Peter Alfeld
Journal: Math. Comp. 35 (1980), 1173-1176
MSC: Primary 65L05
DOI: https://doi.org/10.1090/S0025-5718-1980-0583493-4
MathSciNet review: 583493
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Abstract: Stiff systems of ordinary differential equations are characterized by an initial phase in which the solution changes rapidly. Often there is no interest in reproducing this transient phase. A method is proposed for modifying the initial value if the system of differential equations is separably stiff, i.e. is characterized by the occurrence of a few (typically one) large negative real eigenvalues which dominate the others. The modified system does not possess a transient phase, and in the constant coefficient linear case its solution does not differ from that of the original one in the nonstiff components.


References [Enhancements On Off] (What's this?)

  • [1] P. ALFELD & J. D. LAMBERT, "Correction in the dominant space: A numerical technique for a certain class of stiff initial value problems," Math. Comp., v. 31, 1977, pp. 922-938. MR 0519719 (58:24958)
  • [2] P. ALFELD, "A special class of explicit linear multistep methods as basic methods for the correction in the dominant space technique," Math. Comp., v. 33, 1979, pp. 1195-1212. MR 537965 (80h:65045)
  • [3] W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of ODEs," BIT, v. 15, 1975, pp. 10-48.
  • [4] R. D. SKEEL & A. K. KONG, Blended Linear Multistep Methods, Report UIUCDCS-R-76-800, Department of Computer Science, University of Illinois at Urbana-Champaign, 1976. MR 0461922 (57:1904)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0583493-4
Keywords: Stiff ordinary differential equations, numerical analysis, separably stiff systems, transient phase
Article copyright: © Copyright 1980 American Mathematical Society

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