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The Stability of the {theta}-methods in the Numerical Solution of Delay Differential Equations

Authors:	Liu M Z; SPIJKER M N

Institution:	Department of Mathematics and Computer Science, University of Leiden Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

Abstract:	This paper deals with the stability analysis of numerical methodsfor the solution of delay differential equations. We focus onthe behaviour of the one-leg ${theta}$ -method and the linear ${theta}$ -methodin the solution of the linear test equation U'(t)= ${lambda}$ U(t)+µU(t- ${tau}$ ), with ${tau}$ >0 and complex ${lambda}$ ,µ The stability regions forboth of these methods are determined. The regions turn out tobe equal to each other only if ${theta}$ =0 or ${theta}$ =1.

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