Lie-Trotter method for abstract semilinear evolution equations
Numerical Analysis
2012-11-22 v1 Analysis of PDEs
Abstract
In this paper we present a unified picture concerning Lie-Trotter method for solving a large class of semilinear problems: nonlinear Schr\"odinger, Schr\"oginger--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.
Keywords
Cite
@article{arxiv.1211.5111,
title = {Lie-Trotter method for abstract semilinear evolution equations},
author = {Juan Pablo Borgna and Mariano De Leo and Diego Rial and Constanza Sánchez de la Vega},
journal= {arXiv preprint arXiv:1211.5111},
year = {2012}
}
Comments
2 figures in eps format