The nonlinear Schr{\"o}dinger and the Schr{\"o}dinger-Newton equations model many phenomena in various fields. Here, we perform an extensive numerical comparison between splitting methods (often employed to numerically solve these equations) and the integrating factor technique, also called Lawson method. Indeed, the latter is known to perform very well for the nonlinear Schr{\"o}dinger equation, but has not been thoroughly investigated for the Schr{\"o}dinger-Newton equation. Comparisons are made in one and two spatial dimensions, exploring different boundary conditions and parameters values. We show that for the short range potential of the nonlinear Schr{\"o}dinger equation, the integrating factor technique performs better than splitting algorithms, while, for the long range potential of the Schr{\"o}dinger-Newton equation, it depends on the particular system considered.
翻译:非线性Schr\"o"}丁杰和Schr\"o"}丁杰-牛顿方程式在许多领域模拟许多现象。在这里,我们对分解方法(通常用于数字解析这些方程式)和集成因子技术(也称为劳森法)进行了广泛的数字比较。事实上,后者在非线性Schr\"o"}丁杰-牛顿方程式中表现得很好,但还没有对Schr\"o"}丁杰-牛顿方程式进行彻底调查。比较是在一个和两个空间层面进行的,探索不同的边界条件和参数值。我们显示,对于非线性Schr\"o"丁杰方程式的短期潜力而言,集成因子技术比分解算法表现得更好,而对于Schr\"o"}丁德尔-牛顿方程式的远程潜力,则取决于所考虑的特定系统。