有限区间上多辛Preissmann格式及其附加条件

对于有限区间上偏微分方程Hamilton型PDEs的多辛Preissmann格式必须引入附加条件 ,否则对于KdV方程是不能使用的 ,而对于G .B .方程则不能得到正确的结果 .论文分别具体给出了KdV方程和G .B .方程的这种附加条件 .数值实例显示使用附加条件后由该格式得到的数值解表示的孤立子演化过程和其对应理论解表示的该过程是一致的 ,且格式是长时间数值稳定的

Multi-symplectic Preissmann Scheme in Finite Interval and Its Complementary Condition

The multi symplectic Preissmann scheme for the Hamiltonian PDEs of certain PDE in finite interval must have complementary condition to it, othewise it can not be used for the KdV equation and no proper results can be achieved for G.B.equations. Here the complementary condition is given for the KdV and G.B. equation, respectively. The numerical experiments of the Preissmann scheme with the complementary condition in finite intervals show that the temporal evolution of the solitons coincide with the theoratical ones very well and that the scheme is numerically stable over long time.