Schrdinger方程的时空有限元方法与守恒性  

Space-Time Finite Element Method for the Schrodinger Equation and Its Conservation

作　　者：汤琼[1,2] 陈传淼[1] 刘罗华[2] 吕和祥（推荐） 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081 [2]株洲工学院信息与计算科学系,株洲412008 [3]不详

出　　处：《应用数学和力学》2006年第3期300-304,共5页Applied Mathematics and Mechanics

基　　金：国家973基金资助项目(G1999032804)

摘　　要：对非线性Schr dinger常微分方程,利用常微分方程连续有限元法证明了能量守恒;对非线性Schr dinger偏微分方程利用时空都连续的全离散有限元方法证明了能量积分守恒和利用空间连续、时间间断的有限元法得到电荷近似守恒,误差为高阶量.并在数值计算上探讨了守恒性和近似程度,结果与理论相吻合.Energy conservation of non-linear Schroedinger ordinary differential equation was proved through using ordinary differential equation＇s continuous finite element methods ;Energy integration conservation was proved through using space-time all continuous fully discrete finite element methods and electron nearly conservation with higher order error through using time discontinuous only space continuos finite element methods of non-linear Schroedinger partial equation. The numerical results are in accordance with the theory.

关 键 词：非线性SCHROEDINGER方程 时空有限元方法 能量积分 守恒性 

分 类 号：O242.21[理学—计算数学]