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Implicit-explicit multistep finite element methods for nonlinear parabolic problems. (English) Zbl 0896.65066
The work focuses on the implicit-explicit multistep finite element method for nonlinear parabolic problems. Particularly, the following aspects are covered: the analysis of a simple one-step semi-explicit scheme of first-order accuracy, general multistep schemes of higher accuracy, the results of three applications: the Kuramoto-Sivashinsky equation and the Cahn-Hilliard equation in one dimension, and a class of reaction-diffusion equations in $$\mathbb{R}^s$$, $$s= 2,3$$.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 35K55 Nonlinear parabolic equations 35K57 Reaction-diffusion equations 34A34 Nonlinear ordinary differential equations and systems
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