解四阶杆振动方程的精细时程积分法  

Precise time-integration method for solving four-order rod vibration equation

作　　者：金承日[1] 王玉兰[1] 刘明珠[2] 

机构地区：[1]哈尔滨工业大学(威海)数学系,山东威海264209 [2]哈尔滨工业大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工业大学学报》2005年第8期1043-1045,共3页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金资助项目(10271036);哈尔滨工业大学(威海)校基金资助项目(2002-15;14)

摘　　要：对于四阶杆振动方程初值和周期边界值问题,提出了截断误差阶为O(Δx6)的精细时程积分法.由于该方法是半解析方法,在时间域上可以精确计算,本方法不仅精确度高,还无条件稳定.数值算例进一步验证了上述结论,而且对大的时间步长和长时间计算均有效,是一种很实用的方法.The precise time-integration method is proposed for solving four-order rod vibration equation with initial condition and periodic boundary condition. The local truncation error of the method is O（Ax^4）. The method is a semi-analytical method, hence it can be accurately solved on time domain, and it is unconditionally stable. Numerical example is given finally, the results show that the method has high accuracy even for very large time-step sizes （e. g. At = 2） , and the method has excellent long-time numerical behavior.

关 键 词：四阶杆振动方程 精细时程积分法 无条件稳定 截断误差 长时间计算 

分 类 号：O241.8[理学—计算数学]