%0 Journal Article
%T Comparison of Splitting Methods for Deterministic/Stochastic Gross¨CPitaevskii Equation
%J Mathematical and Computational Applications | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/mca24030076
%X In this paper, we discuss the different splitting approaches to numerically solve the Gross¨CPitaevskii equation (GPE). The models are motivated from spinor Bose¨CEinstein condensate (BEC). This system is formed of coupled mean-field equations, which are based on coupled Gross¨CPitaevskii equations. We consider conservative finite-difference schemes and spectral methods for the spatial discretisation. Furthermore, we apply implicit or explicit time-integrators and combine these schemes with different splitting approaches. The numerical solutions are compared based on the conservation of the L 2 -norm with the analytical solutions. The advantages of the novel splitting methods for large time-domains are based on the asymptotic conservation of the solution of the solitonˇŻs applications. Furthermore, we have the benefit of larger local time-steps and therefore obtain faster numerical schemes. View Full-Tex
%U https://www.mdpi.com/2297-8747/24/3/76