摘要
针对一类带有初边值问题变系数扩散方程,利用相似变换法(伸缩变换)将偏微分方程化成带有初始条件的常微分方程,利用降阶法求出该常微分方程的解析解,从而得到变系数扩散方程的解析解的一般形式.最后通过举例,利用Matlab作出数值解与解析解图像比较,验证解析解形式的正确性.
For a type of variable coefficient diffusion equation with initial boundary value problems,the similarity transformation method(scaling transformation)is used to transform the partial differential equation into an ordinary differential equation with initial conditions.The analytical solution of the ordinary differential equation is obtained using the reduction method,thus obtaining the general form of the analytical solution of the variable coefficient diffusion equation.Finally,by giving examples and using Matlab to compare numerical and analytical solution images,the correctness of the analytical solution form is verified.
作者
夏鹏
XIA Peng(Wuxi Tourism and Trade Branch,Jiangsu Union Technical Institute,Wuxi Jiangsu 214045,China)
出处
《四川职业技术学院学报》
2025年第6期165-168,共4页
Journal of Sichuan Vocational and Technical College
基金
江苏省陶行知研究会重点课题“生活教育理念下中职数学对分课堂教学模式的探究实践”(JSTY14706)。
关键词
变系数
扩散方程
相似变换
降阶法
coefficient of variation
diffusion equation
similarity transformation
reduction method
