Linearly implicit methods for nonlinear evolution equations
作者： Georgios Akrivis , Ohannes Karakashian , Fotini Karakatsani
DOI: 10.1007/S00211-002-0432-Y
关键词:
摘要: We construct and analyze combinations of rational implicit explicit multistep methods for nonlinear evolution equations extend thus recent results concerning the discretization parabolic equations. The resulting schemes are linearly include as particular cases implicit–explicit well combination Runge–Kutta extrapolation. establish optimal order error estimates. abstract applied to a third–order equation arising in modelling flow fluidized bed. discretize this space by Petrov–Galerkin method. fully discrete require solving some linear systems advance time with coefficient matrices same all levels.
springer.com
sci-hub.se 参考文章(11)
Ernst Hairer, Gerhard Wanner, Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems ,(1991)
Panagiotis Chatzipantelidis, Explicit multistep methods for nonstiff partial differential equations Applied Numerical Mathematics. ,vol. 27, pp. 13- 31 ,(1998) , 10.1016/S0168-9274(97)00112-8
Georgios Akrivis, Michel Crouzeix, Charalambos Makridakis, Implicit-explicit multistep finite element methods for nonlinear parabolic problems Mathematics of Computation. ,vol. 67, pp. 457- 477 ,(1998) , 10.1090/S0025-5718-98-00930-2
Garth A. Baker, Vassilios A. Dougalis, Ohannes Karakashian, On multistep-Galerkin discretizations of semilinear hyperbolic and parabolic equations Nonlinear Analysis-theory Methods & Applications. ,vol. 4, pp. 579- 597 ,(1980) , 10.1016/0362-546X(80)90094-2
Graeme Fairweather, J. M. Sanz-Serna, I. Christie, A stabilized Galerkin method for a third-order evolutionary problem Mathematics of Computation. ,vol. 55, pp. 497- 507 ,(1990) , 10.1090/S0025-5718-1990-1035932-9
Gary H. Ganser, Donald A. Drew, Nonlinear periodic waves in a two-phase flow model Siam Journal on Applied Mathematics. ,vol. 47, pp. 726- 736 ,(1987) , 10.1137/0147050
Georgios Akrivis, Michel Crouzeix, Linearly implicit methods for nonlinear parabolic equations Mathematics of Computation. ,vol. 73, pp. 613- 635 ,(2003) , 10.1090/S0025-5718-03-01573-4
Ian Christie, G.H Ganser, A numerical study of nonlinear waves arising in a one-dimensional model of a fluidized bed Journal of Computational Physics. ,vol. 81, pp. 300- 318 ,(1989) , 10.1016/0021-9991(89)90210-6
Vidar Thomée, Galerkin Finite Element Methods for Parabolic Problems ,(1984)
Larry L. Schumaker, Spline Functions: Basic Theory ,(1993)