摘要
探讨扩散方程有界区域只含空间变量的源项识别反问题,基于Tikhonov正则化法提出了迭代正则化法,给出了精确解和正则化解的误差估计,通过选取适当的迭代数,迭代正则化法的源项恢复效果优于Tikhonov正则化法。
The inverse problem of source term identification for a bounded region has been discussed,where the source term depends only on spatial variables.Based on the Tikhonov regularization method,an iterative regularization method is proposed,and the error estimates between the exact solution and the regularization solution are given.By selecting the appropriate iteration number,the source recovery effect of the iterative regularization method is superior to that of the Tikhonov regularization method.
作者
郑江澎
冯立新
ZHENG Jiangpeng;FENG Lixin(China-Russian Joint Graluate Sehool,Heilongiang University,Harbin 150080,China;Department of Meehanics and Mathematics,Novosibirsk State University,Novosibirsk 630090,Russia;School of Mathematical Science,Heilongjiang University,Harbin 150080,Chima)
出处
《黑龙江大学自然科学学报》
CAS
2020年第5期535-543,共9页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(11871198)。
关键词
扩散方程
源项识别反问题
迭代正则化
误差估计
diffusion equation
inverse problem of source term identification
iterative regularization
error estimation
