Using a general computational framework, we derive an optimal error estimate in the $L_2$ norm for a semi discrete method based on high order B-splines Galerkin spatial discretizations, applied to a coupled nonlinear Schrödinger system with cubic nonlinearity. A fully discrete method based on a conservative nonlinear splitting Crank-Nicolson time step is then proposed; and conservation of the mass and the energy is theoretically proven. To validate its accuracy in space and time, and its conservation properties, several numerical experiments are carried out with B-splines up to order 7.

中文翻译：

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耦合非线性薛定谔系统的高阶结构保持B样条Galerkin方法的统一框架

使用通用计算框架，我们在 ${升}_2$基于高阶 B 样条伽辽金空间离散化的半离散方法的范数，应用于具有三次非线性的耦合非线性薛定谔系统。然后提出了一种基于保守非线性分裂Crank-Nicolson时间步长的全离散方法；理论上证明了质量和能量守恒。为了验证其在空间和时间上的准确性及其守恒性质，使用 B 样条进行了多项数值实验，最高可达 7 阶。