The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
- 1 January 1990
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 10 (1) , 31-48
- https://doi.org/10.1093/imanum/10.1.31
Abstract
This paper deals with the stability analysis of numerical methods for the solution of delay differential equations. We focus on the behaviour of the one-leg θ-method and the linear θ-method in the solution of the linear test equation U'(t)=λU(t)+μU(t - τ), with τ>0 and complex λ,μ The stability regions for both of these methods are determined. The regions turn out to be equal to each other only if θ=0 or θ=1.Keywords
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