抛物型微分方程的可视化讨论  

Visualization Analysis on Parabolic Differential Equations

作　　者：廉海荣 方鑫宇 刘明柱[2] 陈长夫 江国明[3] LIAN Hai-rong;FANG Xin-yu;LIU Ming-zhu;CHEN Chang-fu;JIANG Guo-ming(School of Science,China University of Geosciences,Beijing 100083,China;School of Water Resources and Environment,China University of Geosciences,Beijing 100083,China;School of Geophysics and Information Technology,China University of Geosciences,Beijing 100083,China)

机构地区：[1]中国地质大学(北京)数理学院,北京100083 [2]中国地质大学(北京)水资源与环境学院,北京100083 [3]中国地质大学(北京)地球物理与信息技术学院,北京100083

出　　处：《数学的实践与认识》2021年第24期304-310,共7页Mathematics in Practice and Theory

基　　金：中国地质大学(北京)2020年度本科教育质量提升计划建设项目(HHSKE202018)。

摘　　要：研究了几类整数阶与分数阶抛物型方程的可视化问题,包括在多类初边界条件下的一维热传导方程的解析解、高维抛物型方程的数值解和一维分数阶扩散方程的半解析解等,并用MATLAB对几类定解问题进行了可视化实验.The virtual experiments on parabolic equation are discussed subject to different initial and boundary conditions.The prototypical models include the analytical solutions of one-dimensional homogeneous heat conduction equation,the finite element solutions from PDETOOL,the finite difference solutions of high-dimensional model and the semi-analytical solutions fractional diffusion equation.Some experiments are realized by MATLAB.

关 键 词：热传导方程 解析解 数值解 可视化 

分 类 号：O175.26[理学—数学]