General splitting methods for abstract semilinear evolution equations (Q2257624)

A unified approach concerning general splitting methods for solving a large class of semilinear problems is presented. The method is suitable to study the nonlinear Schrödinger equation, the Schrödinger-Poisson equation, and the Gross-Pitaevskii equation. A convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and it is based on Lipschitz estimates for the nonlinearity. Under mild regularity requirements on the initial datum the authors show the linear convergence of the method.