Linearly implicit methods for nonlinear evolution equations (Journal article)

Akrivis, G./ Karakashian, O./ Karakatsani, F.

We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear evolution equations and extend thus recent results concerning the discretization of nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particular cases implicit-explicit multistep schemes as well as the combination of implicit Runge-Kutta schemes and extrapolation. We establish optimal order error estimates. The abstract results are applied to a third-order evolution equation arising in the modelling of flow in a fluidized bed. We discretize this equation in space by a Petrov-Galerkin method. The resulting fully discrete schemes require solving some linear systems to advance in time with coefficient matrices the same for all time levels.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Χημείας
Keywords: explicit multistep methods,parabolic equations,waves,model
ISSN: 0029-599X
Link: <Go to ISI>://000183520000001
Appears in Collections:Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά)

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