【摘要】 对于抛物型方程 t- 2 x22u≡ 2u t2-2 3u t x2+ 4u x4=0的初始值与周期边值问题,提出了局部截断误差阶为O(Δx4)的精细时程积分法.由于这种方法是半解析方法,在时间域上可以精确计算,所以本方法不仅精度高,而且还绝对稳定.文末的数值算例进一步表明,精细积分法对大的时间步长和长时间计算均有效,因此是一种很实用的方法.更多还原

【Abstract】 A precise time-integration method is proposed for solving a higher-order parabolic equation with initial conditions and periodic boundary conditions.The local truncation error of the method is O(△x~4).As this is a semi-analytical method,the equation can be solved in the time domain with high accuracy and unconditional stability.Finally,a numerical example is given.Results show that this method has high accuracy even for very large time-step sizes,and possesses excellent long-time numerical calculation behavior.更多还原