非齐次热方程侧边值问题的一种迭代方法

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (6): 145-150.

非齐次热方程侧边值问题的一种迭代方法

熊向团^*,乔宇

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2020-10-20 出版日期:2021-12-28 发布日期:2021-12-28
通讯作者: 熊向团(1977-),男,湖北武汉人,教授,博导.Email:xiongxt@fudan.edu.com
基金资助:
国家自然科学基金(11661072)

An iterative method for inhomogeneous heat equation of sideways problem

XIONG Xiang-tuan, QIAO Yu

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2020-10-20 Online:2021-12-28 Published:2021-12-28

摘要/Abstract

摘要： 探讨非齐次热方程侧边值问题,这类问题是严重不适定的. 应用迭代正则化方法,得到问题的一个正则近似解,并分别在先验和后验正则化参数选取规则下给出正则解与精确解之间的Hlder型误差估计,数学实验表明使用迭代正则化方法求解这类问题是有效的.

关键词: 非齐次热方程, 侧边值问题, 不适定, 迭代正则化, 误差估计

Abstract: The sideways problem of nonhomogeneous heat equation is discussed, which is seriously ill-posed. By using the iterative regularization method, a regular approximate solution of the problem is obtained, and the Hlder type error estimate of this solution relative to the exact solution is given under a prior and a posterior regularization parameter selection rules, which shows that the iterative regularization method is effective to solve such problems.

Key words: inhomogeneous heat equation;sideways problem, ill-posed, iterative regularization, error estimate

中图分类号:

O241.1

熊向团,乔宇. 非齐次热方程侧边值问题的一种迭代方法[J]. 兰州理工大学学报, 2021, 47(6): 145-150.

XIONG Xiang-tuan, QIAO Yu. An iterative method for inhomogeneous heat equation of sideways problem[J]. Journal of Lanzhou University of Technology, 2021, 47(6): 145-150.

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