Recently, several numerical methods based on the radial basis functions have been applied to solving differential equations. Many researchers have employed the radial basis functions collocation technique and its improvements to get more accurate and efficient numerical solutions. The Schrödinger equations have several applications in the optic and laser. Accordingly, several numerical procedures have been proposed. In this paper, we present a new numerical algorithm based on the time-split approach, and rational radial basis functions collocation method. First, a second-order time-split approach is used to discretize the time variable. In this stage, the linear and nonlinear terms are separated. The linear term is solved by using a collocation technique based on the rational approach, the radial basis functions, and the partition of unity. The nonlinear term is does not have a differential operator thus we will only insert approximate solutions into it. Finally, several numerical examples have been reported to show the stability, convergence, and accuracy of the proposed numerical algorithm.

中文翻译：

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基于N耦合非线性薛定谔方程和统一方法有理RBF划分的光孤子

最近，几种基于径向基函数的数值方法已被应用于求解微分方程。许多研究人员采用径向基函数搭配技术及其改进来获得更准确、更高效的数值解。薛定谔方程在光学和激光领域有多种应用。因此，已经提出了几种数值程序。在本文中，我们提出了一种基于时间分割方法和合理径向基函数配置方法的新数值算法。首先，使用二阶时间分割方法来离散化时间变量。在此阶段，线性项和非线性项被分离。线性项通过使用基于有理方法、径向基函数和单位划分的配置技术来求解。非线性项没有微分算子，因此我们只会在其中插入近似解。最后，几个数值例子显示了所提出的数值算法的稳定性、收敛性和准确性。