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dinger Equation with Collapse Potential Term

作　　者：周晶晶[1] 孔令华[1] 黄红[1] 黄晓梅[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2013年第6期633-636,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11301234;11271171);江西省自然科学基金(20114BAB201011);2010年江西师范大学青年成长基金资助项目

摘　　要：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 Schrodinger equation with collapse term by discretizing spatial direction with compact method. The scheme is not only with high accuracy, but also un- conditionally 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.

关 键 词：薛定谔方程 高阶紧致格式 守恒律 

分 类 号：O241.8[理学—计算数学]