High order time-splitting methods for irreversible equations

M. DE LEO; CONSTANZA S. F. DE LA VEGA; D. RIAL

IMA JOURNAL OF NUMERICAL ANALYSIS

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2015

0272-4979

In this work, high order splitting methods of integration without negative steps are shown which can be used in irreversible problems, like reaction?difussion or complex Ginzburg?Landau equations. The methods consist in a 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 thatthe computation time can be significantly reduced using multiple processors. Convergence results of these methods are proved for a large kind of semilinear problems, that includes reaction-difussion systems anddissipative perturbation of Hamiltonian systems.