热传导方程解的稳定性以及Matlab数值模拟  

Stability of the Solution of Heat Conduction Equation andMatlab Numerical Simulation

作　　者：郭连红 GUO Lianhong(Guangzhou Panyu Polytechnic,Guangzhou 511483)

机构地区：[1]广州番禺职业技术学院,广州511483

出　　处：《高等数学研究》2024年第1期123-126,共4页Studies in College Mathematics

基　　金：广州番禺职业技术学院2021年科研项目(No.2021KJ17);广州番禺职业技术学院2021年教育教学改革项目(No.2021JG24).

摘　　要：应用能量估计方法,分析一类热传导方程的解对初始数据的连续依赖性,再应用Matlab中的偏微分方程工具箱PDE Toolbox对一类特殊的热传导方程进行建模求解.通过数值模拟观察温度场的分布和梯度方向的变化,结果显示,靠近热源一侧的分子最先被加热,温度由高温的一侧向低温一侧变化,在经过一段时间后,整个温度场将逐渐趋于稳态.Using the energy estimation method,the continuous dependence of the solution of a kind of heat conduction equation to the initial data is analyzed.The PDE Toolbox of Matlab is used to solve a special kind of heat conduction equation.Through the numerical simulation,we observe the change of the temperature field distribution and gradient direction,which shows that the molecules are heated first near the heat source side,the temperature flows from high side to low side,and the whole temperature field gradually tends to be steady after a period of time.

关 键 词：热传导方程 能量估计法 MATLAB模拟 

分 类 号：O175.24[理学—数学]