三维非线性Schrodinger方程的六阶精度紧致ADI分裂方法  

Sixth-order Compact ADI Splitting Method for the Nonlinear Schrodinger Equation in Three-dimensions

作　　者：热娜·阿斯哈尔[1] 黄鹏展[1] 冯新龙[1] Rena Eskar;HUANG Peng-zhan;FENG Xin-long(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2020年第1期229-237,共9页Mathematics in Practice and Theory

基　　金：新疆大学优秀博士研究生创新项目(XJUBSCX-2013005);国家自然科学基金(11362021,11801485,11861067).

摘　　要：提出了一种结合二阶Strang分裂技术的六阶紧致交替方向隐式方法,用于求解三维非线性Schrodinger方程.方法在时间上具有二阶精度,在空间上具有六阶精度.稳定性分析表明,方法是无条件稳定的.通过数值实验验证了方法满足守恒律,并为三维非线性Schrodinger方程提供了精确、稳定的解.In this paper,we propose a sixth-order compact alternating direction implicit(ADI) method combined with second-order Strang splitting technique for solving the three-dimensional nonlinear Schrodinger equation.The method is second-order accurate in time and sixth-order accurate in space.Stability analysis is demonstrated that the method is unconditionally stable.Numerical results show that these schemes preserve the conservation laws and provide accurate and stable solutions for the three-dimensional nonlinear Schrodinger equation.

关 键 词：非线性SCHRODINGER方程 六阶精度紧致ADI方法 守恒律 稳定性 分裂法 

分 类 号：O175.29[理学—数学]