Mariano De Leo

Juan Pablo Borgna, Mariano De Leo, Diego Rial et al.

In this paper we present a unified picture concerning Lie-Trotter method for solving a large class of semilinear problems: nonlinear Schrödinger, Schröginger--Poisson, Gross--Pitaevskii, etc. This picture includes more general schemes such as Strang and Ruth--Yoshida. The convergence result is presented in suitable Hilbert spaces related with the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity we show the linear convergence of the method.

Mariano De Leo, Diego Rial, Constanza Sanchez de la Vega

In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of Lie-Trotter schemes with different steps. We prove convergence of this methods for a large class of semi-linear problems, that includes Hamiltonian and reaction-diffusion systems.