Schrödinger方程的时空有限元方法与守恒性

基金项目: 国家973基金资助项目(G1999032804)

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

1.
Department of Mathematics and Computing Science, Hunan Normal University, Changsha 410081, P. R. China;

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．
- 非线性Schr?dinger方程 /
- 时空有限元方法 /
- 能量积分 /
- 守恒性
Abstract: Energy conservation of non-linear Schrêdinger 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 Schrêdinger partial equation.The numerical results are in accordance with the theory.
- non-linear Schrê /
- dinger equation /
- space-time finite element method /
- energy integration

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