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Marginal stability and stabilization in the numerical integration of ordinary differential equations


Author: H. Brunner
Journal: Math. Comp. 24 (1970), 635-646
MSC: Primary 65.61
MathSciNet review: 0273821
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Abstract: Strongly stable and consistent multistep methods with maximum order are subject to marginal (or weak) stability. In this paper we introduce modified multistep methods whose coefficients depend linearly on the stepsize $ h$ and a parameter $ L$ in such a way that the order of the original method is not decreased. By choosing $ L$ in a suitable manner (depending essentially on $ {f_y}(x,y)$ of the differential equation $ y' = f(x,y)$ and on the growth parameters of the multistep method), marginal stability can be eliminated.


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

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0273821-5
Keywords: Nonlinear ordinary differential equations of order one, numerical solution, optimal multistep methods, marginal stability, stabilization
Article copyright: © Copyright 1970 American Mathematical Society