【摘要】 提出由第三类生成函数法构造Schr dinger方程i u t= 2u x2的高精度辛格式.首先给出它的典则Hamilton方程组;然后成功地克服了本质上是困难的高阶变分导数的计算,并利用第三类生成函数法得到在时间方向具有任意阶精度的半离散方程,进而得到原始方程相关的修正方程的离散形式,最后得到各种精度的辛格式.数值结果表明该格式是有效的.更多还原

【Abstract】 The author presents a new method to construct the symplectic schemes with high accuracy by the third type generating functions for the Schrdinger type equation iut=uxx. First,the Schrdinger type equation is written into the canonical Hamiltonian system; Secondly,overcoming successfully the essential difficult on the calculation of high order variations ,we get the semidiscretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating functions,furthermore, the related modified equation of original equation is obtained from the semidiscretization. Finally,symplectic schemes with arbitrary order of accuracy are obtained. Numerical results are also presented to show the effectiveness of the scheme.更多还原