计算机技术与发展

偏微分方程的数值解法在数值分析中占有很重要的地位,很多科学技术问题的数值计算包括了偏微分方程的数值解问题。在学习初等函数时,总是先画出它们的图形,因为图形能帮助了解函数的性质。而对于偏微分方程,画出它们的图形并不容易,尤其是没有解析解的偏微分方程,画图就显得更加不容易了。为了从偏微分方程的数学表达式中看出其所表达的图形、函数值与自变量之间的关系,通过MATLAB编程,数值求解了泊松方程,并将其结果可视化,给出了解析解与数值解的误差。

The numerical solution of partial differential equations plays an important role in numerical analysis,the numerical calculation of many science technology includes the numerical solution problem of the partial differential equations. In the study of primary function, always draw their graphics,because the graphics can help to understand the nature of the function. But for the partial differential equations,painting their graphics will not be easy,in particular for the partial differential equations that have no analytical solution,drawing is more difficult. In order to look out the relationship between graphics and function values and variables from the partial differential equations,through MATLAB programming,soluted the Poisson equation with numerical method,and visualizated the results. Painted the error between analytical solutions and numerical solutions.