A stabilization of multistep linearly implicit schemes for dissipative systems

Authors:
Takayasu Matsuo;Daisuke Furihata
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 3
Cited 0

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

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Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

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Abstract

We consider numerical integration of dissipative gradient systems. For such systems, a class of special, stable integrators that strictly maintain dissipation is known, but they generally yield expensive fully implicit schemes, and when the system is large, linearization is indispensable for practical efficiency. However, this can in turn destroy the originally expected stability, and so far no effective principle has been formulated for a stable linearization. In this note, we point out that the behavior of the linearized schemes can be understood from a dynamical systems theory viewpoint and propose a simple principle for a stable linearization.