一维波动方程的计算模拟  

The Numerical Simulation of One-dimensional Wave Equation

作　　者：斯小琴 陈大伟 SI Xiaoqin;CHEN Dawei(Foundation Department,Anhui Jianzhu University of Urban Construction College,238076,Hefei,Anhui,China;School of Physical Sciences,University of Science and Technology of China,230026,Hefei,Anhui,China)

机构地区：[1]安徽建筑大学城市建设学院基础部,安徽合肥238076 [2]中国科学技术大学物理学院,安徽合肥230026

出　　处：《淮北师范大学学报（自然科学版）》2022年第3期22-25,共4页Journal of Huaibei Normal University：Natural Sciences

基　　金：中西部高等学校青年骨干教师国内访学项目;安徽高校自然科学研究重大项目(KJ2019ZD64);安徽高校自然科学研究重点项目(KJ2020A1211)。

摘　　要：借助计算机辅助分析一维波动方程的特征,应用有限差分法求出一维波动方程的数值解,借助于基本办公软件EXCEL迭代数据,并通过Origin将巨大量的数值解数据模拟成波动图形.直观得到含初始、边界条件的混合问题各点的振动情况,简明、形象地反映一维波动的特征.该数值解方法在一定精度要求范围内具有可靠性,以及借助计算机辅助分析的重要性,避免对微分方程的繁琐求解及复杂的计算机编程,在解决实际相关问题中有一定的参考价值.The characteristics of one-dimensional wave equation are analyzed with the help of computer.The numerical solution of one-dimensional wave equation is obtained by using the finite difference method.With the help of the basic office software Excel,a large number of numerical solution data are simulated into wave graphics through origin.The vibration of each point of the mixed problem with initial and boundary conditions is obtained intuitively,which concisely and vividly reflects the characteristics of one-dimensional wave.It shows that the numerical solution method has reliability in a certain accuracy range,and the importance of computer-aided analysis.This method avoids the tedious solution of differential equations and complex computer programming,and has a certain reference value in solving related practical problems.

关 键 词：波动方程 数值解 计算模拟 

分 类 号：O415.6[理学—理论物理]