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波动方程的精细逐步积分法
引用本文:王金东,高鹏,陈浩然.波动方程的精细逐步积分法[J].上海力学,2000,21(3):316-321.
作者姓名:王金东  高鹏  陈浩然
作者单位:[1]大庆石油学院机械系,黑龙江安达151400 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024
摘    要:应用现有的波动方程求解方法解决工程实际问题尚存在一定的局限性。本文在结构动力方程精细逐步积分的基础上,提出了波动方程初边值问题的精细逐步积分法,并分别给出了不同边界条件下的精细逐步积分格式。此数值方法虽然是显式积分方法,却是无条件稳定的。分别用精细逐步积分法和其它已有的方法对两个算例进行了计算,一个是有解析解的例子,该例验证了此方法的准确性,另一个例子是求解由波动方程及初始条件和边界条件组成的有杆抽油系统预测模型,此例验证了精细逐步积分法的高效性。

关 键 词:波动方程  差分法  偏微分方程  精细逐步积分法
修稿时间:1999年11月1日

Precise Direct Integration Method for Wave Equation
WANG Jin-dong,GAO Peng,CHEN Hao-ran.Precise Direct Integration Method for Wave Equation[J].Chinese Quarterly Mechanics,2000,21(3):316-321.
Authors:WANG Jin-dong  GAO Peng  CHEN Hao-ran
Abstract:The known numerical methods of the wave equation have some shortcoming when applied to practical problems. Based on the precise time-integration method for structural dynamic systems, a precise direct integration method is proposed for the initial-boundar-value problem of the wave equation, and the precise direct integration forms under the different boundary conditions are given in the paper. Though the numerical method is an explicit integral method, it is unconditionally steady. Two examples are calculated with the precise direct integration, the implicit difference and the explicit difference respectively. The first example that has an analytical solution testifys to the accuracy of the precise direct integration method. The second example is used to solve the predicting model of sucker-rod pumping system, in which the predicting model consists of the wave equation and the initial-boundary-value conditions. It shows the highly efficient characteristic of the precise direct integration method.
Keywords:wave equation  difference method  step-by-step integration method
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