Stability of multistep methods for delay differential equations

Wiederholt, Lawrence F.

doi:10.1090/S0025-5718-1976-0398132-4

Stability of multistep methods for delay differential equations
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by Lawrence F. Wiederholt PDF

Math. Comp. 30 (1976), 283-290 Request permission

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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