解(■~2U)/(■T^2)=A(■~4U)/(■T^2■X^2)+B(■~2U)/(■T■X)+C(■~4U)/(■X^4)的周期问题的精细积分法

Precise integration method for solving the equation (?)~2u/(?)t^2=a(?)~4u/(?)t^2(?)x^2+b(?)~2u/(?)t(?)x+c(?)~4u/(?)x^4with periodic boundary condition

对于方程■2U/■T2=A■4U/■T2■X2+B■2U/■T■X+C■4U/■X4的初始值与周期边值问题,利用四阶差分化为关于时间变量的常微分方程组,然后采用精细时程积分法．通过对精细积分法递推过程的误差分析,发现该方法能获得高精度数值结果的根本原因是:数值计算的相对误差不随递推过程的进行而扩散．

On the equation the second derivative of u to t=a（the second derivative of the second derivative of u to x to t）＋b（the derivative of u to x to t）＋c（the fourth derivative of u to x） with initial condition and periodic boundary condition, asystem of ordinary differential equations to time was built by the four - order difference method, then the precise integration method was used to solve the system. By means of error analysis of recursion process of precise integration, it is found that the essential reason of obtaining the high precise numerical results of exponential matrix in the precise integration method is that the relative error of numerical computation is not enlarged in a whole recurrent process.