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M. Z. Liu, M. N. SPIJKER, The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations, IMA Journal of Numerical Analysis, Volume 10, Issue 1, January 1990, Pages 31–48, https://doi.org/10.1093/imanum/10.1.31
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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.
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© 1989 Oxford University Press
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