具有坍塌势的4阶薛定谔方程的紧致守恒格式
Compact and Conserving Scheme of Fourth-Order Schr(o)dinger Equation with Collapse Potential Term

利用紧致方法离散4阶薛定谔方程的空间导数,构造出具有坍塌势的4阶薛定谔方程的紧致守恒格式.理论分析表明该格式具有精度高、模版小的特点,且保持离散的电荷守恒律以及能量守恒律.最后通过数值实验验证理论分析的正确性.
The compact and conserving scheme is presented to solve fourth-order Schr?dinger equation with collapse term by discretizing spatial direction with compact method.The scheme is not only with high accuracy,but also unconditionally stable.Moreover,it is proved that the scheme preserves discrete charge conservation law and energy conservation law.Detailed numerical results suggest that the scheme is efficient and consistent with our theoretical analysis