解一类时间分数阶逆扩散问题的分数阶Tikhonov正则化方法OA
Fractional Order Tikhonov Regularization Method for Solving a Class of Time Fractional Order Inverse Diffusion Problems
利用分数阶Tikhonov正则化方法讨论一类时间分数阶扩散方程逆问题,分别给出先验条件和后验条件下正则化参数的选取准则,并给出该方法收敛性的严格证明.数值实验结果表明,分数阶Tikhonov正则化方法解该问题有效.
We discussed a class of inverse problem of time fractional order diffusion equations by using the fractional order Tikhonov regularization method.We gave selection criteria for the regularization parameter under prior and posterior conditions,and gave rigorous proofs of the convergence of the method.Numerical experimental results show that the fractional order Tikhonov regularization method is effective in solving this problem.
刘云泽;冯立新
黑龙江大学数学科学学院,哈尔滨 150080黑龙江大学数学科学学院,哈尔滨 150080
数理科学
分数阶逆扩散问题分数阶Tikhonov正则化先验和后验参数选取规则误差估计
fractional order inverse diffusion problemfractional order Tikhonov regularizationselection rules for prior and posterior parameterserror estimates
《吉林大学学报（理学版）》 2026 (1)
13-20,8
国家自然科学基金(批准号:12101205)和黑龙江省自然科学基金(批准号:PL2024A010).
评论