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Georgios Akrivis, Stability of implicit and implicit–explicit multistep methods for nonlinear parabolic equations, IMA Journal of Numerical Analysis, Volume 38, Issue 4, October 2018, Pages 1768–1796, https://doi.org/10.1093/imanum/drx057
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Abstract
We analyse the discretization of nonlinear parabolic equations in Hilbert spaces by both implicit and implicit–explicit multistep methods and establish local stability under best possible and best possible linear stability conditions, respectively. Our approach is based on suitable quantifications of the non-self-adjointness of linear elliptic operators and a discrete perturbation argument.
nonlinear parabolic equations, quantification of the non-self-adjointness of elliptic operators, implicit and implicit–explicit multistep methods, BDF methods, strong A(0)-stability, A(ϑ)-stability, sharp linear stability conditions, sufficient and necessary stability conditions, sharp stability conditions
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