一种修正的Tikhonov方法求解Helmholtz方程柯西问题
2023-07-28余亚辉李振平
余亚辉 李振平
摘要:考虑矩形区域上Helmholtz方程柯西问题,该问题是一类严重不适定的偏微分方程反问题,它的解不连续依赖于输入数据.使用修正的Tikhonov正则化方法给出了该问题基于分离变量的近似解,并通过先验和后验两种不同的正则化参数选择规则得到了精确解与正则化近似解之间的Hlder型误差估计.
关键词:Helmholtz方程柯西问题;不适定问题;正则化;后验参数选取;误差估计
中图分类号:O 175 文献标志码:A 文章编号:1001-988Ⅹ(2023)04-0029-06
4 结束语
本文使用一种修正的Tikhonov方法求解矩形区域上的Helmholtz方程柯西问题,不仅给出正则化参数的先验选取下精确解与正则化近似解之间的Hlder型误差估计,还给出了正则化参数后验选取规则及误差估计.该方法可能也适用于其他不适定的反问题,这也有待于我们进一步探究.
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