抛物型方程周期问题的高精度精细积分法  

HIGH PRECISION METHOD OF TIME-INTEGRATION FOR SOLVING PARABOLIC EQUATION

作　　者：王玉兰[1] 杜红[2] 王玉荣 

机构地区：[1]内蒙古工业大学理学院,呼和浩特010062 [2]哈尔滨工业大学数学系 [3]呼和浩特第九中学,呼和浩特010038

出　　处：《内蒙古工业大学学报（自然科学版）》2004年第4期245-249,共5页Journal of Inner Mongolia University of Technology：Natural Science Edition

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

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.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.

关 键 词：精细积分法 高阶抛物型方程 无条件稳定 局部截断误差 长时间计算 

分 类 号：O241.8[理学—计算数学]