非线性热传导方程的反演计算  

Inverse Calculation of Nonlinear Heat Conduction Equation

作　　者：杨浩[1] 赵丽玲[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2013年第4期347-353,共7页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：讨论非线性热传导方程确定未知热导率分布的反问题.由于热导率与空间和时间有关,先将非线性方程近似转化成线性方程,再通过中心差分离散,采用步进格式得到求解网格节点温度的迭代方程并讨论迭代方程的数值稳定性,最后结合广义交叉校验(GCV)准则和Tikhonov正则化方法,反演计算出与空间位置和温度有关的热导率.数值模拟结果表明该方法可行有效.This paper discussed the inverse problems of determining unknown heat conductivity distribution by nonlinear heat conduction equation. Because of the links among heat conductivity, space and time, the nonlinear equations were firstly approximately converted into linear equations. Then, through the separation of the equation of center, the paper obtained the iterative equations for solving the temperature of grid nodes with marching method, discussed the numerical stability of the iterative equations, and finally inversely calculated the heat conductivity which concerning space and temperature by combing generalized cross check （GCV） with Tikhonov regularization method. The numerical simulation results show that the treatment is feasible and efficacious.

关 键 词：热传导方程 反问题 正则化方法 

分 类 号：O174.41[理学—数学]