确定热方程未知源问题的超阶正则化方法

Abstract

Abstract:

The problem for determining an unknown source in the heat equation is considered in this paper. We present a Tikhonov regularization method with a super order penalty term to deal with illposedness of the problem. The regularization parameter is chosen by a discrepancy principle and the order optimal error bounds can be obtained for various smooth conditions. The smoothness parameter and the a priori bound of exact solution are not needed in the numerical process. Numerical tests show that the proposed method is effective and stable.

Key words: Ill-posed problem, Super order regularization, Heat equation, Unknown source, Discrepancy principle

CLC Number:

O124

Zhenyu Zhao,Riguang Lin,Zhi Li,Duan Mei. A Super Order Regularization Method for Determination of an Unknown Source in the Heat Equation[J].Acta mathematica scientia,Series A, 2020, 40(3): 717-724.

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$\delta_1$	M2			M1
	$q=2$	$q=4$	$q=8$
1e-1	9.18e-2	8.68e-2	8.90e-2	9.68e-2
1e-2	1.81e-2	1.54e-2	1.47e-2	1.41e-2
1e-3	2.91e-3	2.24e-3	1.98e-3	1.58e-3
1e-4	5.99e-4	2.81e-4	2.25e-4	1.75e-4

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A Super Order Regularization Method for Determination of an Unknown Source in the Heat Equation

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