一类热传导方程逆时反问题的数值解法  

A numerical method for solving a backward heat conduction equation

作　　者：葛美宝[1] 徐定华[2] 

机构地区：[1]浙江理工大学科技与艺术学院,浙江杭州311121 [2]浙江理工大学理学院,浙江杭州310018

出　　处：《浙江师范大学学报（自然科学版）》2011年第1期59-63,共5页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(NSFC10561001NSFC11071221);浙江理工大学科研基金资助项目(0613263);浙江理工大学科技与艺术学院2008年大学数学教学团队项目(kyjxtd0801);浙江理工大学科研项目(2010KY009)

摘　　要：讨论一类热传导方程逆时反问题(BHCP)的数值解法.中心差分法的思想是基于对原问题只进行空间离散,转化为一个不适定的常微分方程组的初值问题,然后利用变量变换把该问题转化为一个适定的常微分方程组的初值问题,最后利用Runge-Kutta方法进行数值求解.数值结果说明了数值解与精确解吻合良好.A numerical method of a backward heat conduction equation was discussed.The idea of central difference was based on the original problem of the space discreting only,and converted into an ill-posed ordinary differential equations with initial conditions.Then by employing the variable transformation,it was converted into a well-posed ordinary differential equations with initial conditions,which could be numerically solved by Runge-Kutta method.The Numerical results showed that the numerical solution were consistene with the exact solution.

关 键 词：热传导方程 反问题 中心差分法 数值解法 

分 类 号：O175.26[理学—数学]