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

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.