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Mathematics of Computation

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Stability of multistep methods for delay differential equations

Author: Lawrence F. Wiederholt
Journal: Math. Comp. 30 (1976), 283-290
MSC: Primary 65Q05; Secondary 65L05
MathSciNet review: 0398132
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Abstract: The absolute and relative stability of linear multistep methods for a finite step size is studied for delay differential equations. The differential equations are assumed linear and the delays a constant integer multiple of the step size. Computable conditions for stability are developed for scalar equations. Plots of the stability regions for several common multistep methods are included. For the integration methods considered, the stability regions for delay differential equations are significantly different from the stability regions for ordinary differential equations.

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Keywords: Delay (or retarded) differential equations, stability of integration methods
Article copyright: © Copyright 1976 American Mathematical Society