一维热传导方程数值解的计算机仿真与研究  

Computer simulation and research on numerical solution of one-dimensional heat conduction equation

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

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

出　　处：《青岛理工大学学报》2023年第5期169-174,共6页Journal of Qingdao University of Technology

基　　金：中西部高等学校青年骨干教师国内访学项目;高校优秀青年人才支持计划一般项目(gxyq2022186);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了一维热传导方程数值解、精确解及两种解的差的绝对值和最大误差。运用古典显示差分法和基本办公软件Excel循环迭代功能计算了该格式下一维热传导方程的数值解,通过Origin绘图将数值可视化以使对比更直观。比较表明,该数值解方法在满足一定的精度要求范围内能得到符合实际的结果。结合使用Excel迭代计算功能,避免了微分方程的繁琐求解及计算机的复杂编程,给解决实际问题带来较大的便利。In this study,the numerical solution and exact solution of one-dimensional heat conduction equation,and the absolute value and maximum error of the difference between these two solutions are analyzed by computer.By using the classical display difference method and the circular iteration function of the basic office software Excel,the numerical solution of one-dimensional heat conduction equation under this scheme is calculated.The values are visualized through the origin plot to make the comparison more intuitive.The comparison shows that the numerical solution method can get practical results within a certain accuracy range.Combined with the iterative calculation function of Excel,the tedious solution of differential equations and complex computer programming are avoided,which brings great convenience to the solution of practical problems.

关 键 词：数值分析 数值解 差分法 热传导方程 

分 类 号：O415.6[理学—理论物理]