带有Riemann-Liouville导数的分数阶热传导方程逆源问题的正则化方法

Regularization Method for Inverse Source Problem of FractionalHeat Conduction Equation with Riemann-Liouville Derivative

首先,用Tikhonov正则化方法求解带有Riemann-Liouville导数的分数阶热传导方程逆源问题,得到了包含Mittag-Leffler函数的正则解;其次,对正则解进行收敛性分析,给出先验参数选取下正则解和精确解的误差估计及后验参数选取下正则化参数的取值范围.数值实验结果表明了该正则化方法的有效性.

Firstly,by using Tikhonov regularization method to solve the inverse source problem of the fractional heat conduction equation with Riemann-Liouville derivative,we obtained a regularization solution with Mittag-Leffler function.Secondly,we analyzed the convergence of the regularization solution,gave the error estimate of the regularization and exact solutions under a priori parameter choice rule,and the range of regularization parameter under a posterior parameter choice rule.The numerical experiment results show the effectiveness of proposed regularization method.