Artículos de revistas
High-order time-splitting methods for irreversible equations
Fecha
2016-10Registro en:
de Leo, Mariano Fernando; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; High-order time-splitting methods for irreversible equations
; Oxford University Press; Ima Journal Of Numerical Analysis; 36; 4; 10-2016; 1842-1866
0272-4979
CONICET Digital
CONICET
Autor
de Leo, Mariano Fernando
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
Resumen
In this work, high-order splitting methods of integration without negative steps are shown which can be used in irreversible problems, like reaction–diffusion or complex Ginzburg–Landau equations. These methods consist of suitable affine combinations of Lie–Tortter schemes with different positive steps. The number of basic steps for these methods grows quadratically with the order, while for symplectic methods, the growth is exponential. Furthermore, the calculations can be performed in parallel, so that the computation time can be significantly reduced using multiple processors. Convergence results of these methods are proved for a large range of semilinear problems, which includes reaction–diffusion systems and dissipative perturbation of Hamiltonian systems.