Lubich, Ch. On the stability of linear multistep methods for Volterra convolution equations. (English) Zbl 0543.65095 IMA J. Numer. Anal. 3, 439-465 (1983). 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 Cited in 2 ReviewsCited in 68 Documents MSC: 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 45J05 Integro-ordinary differential equations Keywords:positive definite kernels; linear multistep methods; second kind; Volterra integro-differential equations; linear convolution equation; strong stability; A-stability; completely monotonic kernels PDFBibTeX XMLCite \textit{Ch. Lubich}, IMA J. Numer. Anal. 3, 439--465 (1983; Zbl 0543.65095) Full Text: DOI