【摘要】 基于Hamilton空间体系的多辛理论研究了膜自由振动问题,讨论了构造复合离散多辛格式的方法,并构造了一种典型的9×3点半隐式的多辛复合离散格式,该格式满足多辛守恒律、能量守恒律和动量守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.更多还原

【Abstract】 The multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space were considered.The complex method was introduced and a semi-implicit twenty-seven-point scheme with certain discrete conservation laws-a multi-symplectic conservation law(CLS),an energy conservation law(ECL) as well as a momentum conservation law(MCL)-is constructed to discrete the PDEs that are derived from the membrane free vibration equation.The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior.更多还原