CAJ | 학술논문

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。
편미분방정적수치해법재수치분석중점유흔중요적지위，흔다과학기술문제적수치계산포괄료편미분방정적수치해문제。재학습초등함수시，총시선화출타문적도형，인위도형능방조료해함수적성질。이대우편미분방정，화출타문적도형병불용역，우기시몰유해석해적편미분방정，화도취현득경가불용역료。위료종편미분방정적수학표체식중간출기소표체적도형、함수치여자변량지간적관계，통과MATLAB편정，수치구해료박송방정，병장기결과가시화，급출료해석해여수치해적오차。
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 equa-tions,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 equa-tions,through MATLAB programming,soluted the Poisson equation with numerical method,and visualizated the results. Painted the error between analytical solutions and numerical solutions.