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A special class of explicit linear multistep methods as basic methods for the correction in the dominant space technique


Author: Peter Alfeld
Journal: Math. Comp. 33 (1979), 1195-1212
MSC: Primary 65L05
MathSciNet review: 537965
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Abstract: A class of explicit linear multistep methods is suggested as basic methods for the CDS schemes introduced in [3]. These schemes are designed for the numerical solution of certain stiff ordinary differential equations, and operate with dominant eigenvalues, and the corresponding eigenvectors, of the Jacobian. The motivation, and the stability analysis for CDS schemes assumes that the eigensystem is constant. Here methods are introduced that perform particularly well if the eigensystem is not constant. In a certain sense the methods introduced here can be considered explicit approximations to the well-known implicit backward-differentiation formulas used by Gear [6] for the stiff option of his o.d.e. solver.


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  • [1] P. ALFELD, "Inverse linear multistep methods for the numerical solution of initial value problems of ordinary differential equations," Math. Comp., v. 33, 1979, pp. 111-124. MR 514813 (80b:65092)
  • [2] P. ALFELD, Correction in the Dominant Space: A New Technique for the Numerical Solution of Certain Stiff Initial Value Problems, Ph. D. Thesis, University of Dundee, 1977.
  • [3] P. ALFELD & J. D. LAMBERT, "Corrections 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)
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  • [6] C. W. GEAR, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N. J., 1971. MR 0315898 (47:4447)
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  • [8] J. D. LAMBERT, Computational Methods in Ordinary Differential Equations, Wiley, New York, 1973. MR 0423815 (54:11789)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0537965-0
Keywords: Ordinary differential equations, numerical analysis, correction in the dominant space, separably stiff systems, interprojection, backward-differentiation formulas
Article copyright: © Copyright 1979 American Mathematical Society