In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a nonlinear Schroedinger equation by solving the linear problem and treating the nonlinear term separately, with a rigorous estimate of the remainder term. Furthermore, we show by means of numerical experiments that such a modified approximation is more efficient than the standard one.
翻译:在本文中,我们提出了一个修改的里型光谱分裂近似值,外部潜力为二次类型。 事实证明,我们可以通过解决线性问题和分别处理非线性术语,对剩余期限进行严格的估计,来比较非线性平方程式的解决方案。 此外,我们通过数字实验来表明,这种修改近似值比标准平方程式的效率更高。