论文标题
应用于schrödinger的方程式的集成因子技术。与拆分方法的比较
Integrating factor techniques applied to the Schrödinger-like equations. Comparison with Split-Step methods
论文作者
论文摘要
非线性Schrödinger和Schrödinger-Newton方程模拟了各个领域的许多现象。在这里，我们在分裂方法（通常用于数值求解这些方程式）和集成因子技术（也称为Lawson方法）之间进行了广泛的数值比较。确实，已知后者在非线性schrödinger方程中表现良好，但尚未对Schrödinger-Newton方程进行彻底研究。比较以一个和两个空间维度进行，探索不同的边界条件和参数值。我们表明，对于非线性schrödinger方程的短范围潜力，整合因子技术的性能要比分裂算法更好，而对于Schrödinger-Newton方程的远距离潜力，它取决于所考虑的特定系统。
The nonlinear Schrödinger and the Schrödinger-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 Schrödinger equation, but has not been thoroughly investigated for the Schrödinger-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 Schrödinger equation, the integrating factor technique performs better than splitting algorithms, while, for the long range potential of the Schrödinger-Newton equation, it depends on the particular system considered.
