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On the stability of linear multistep methods for Volterra convolution equations. (English) Zbl 0543.65095

An application of linear multistep methods for ordinary differential equations to linear Volterra integral equations of the second kind and to Volterra integro-differential equations generates a discrete linear convolution equation. The stability of such methods is investigated in this paper. It is shown that the strong stability, the A-stability and the \(A(\alpha)\)-stability for ordinary differential equations carry over to convolution equations with positive definite or completely monotonic kernels.
Reviewer: S.Filippi

MSC:

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
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