THE LEVENBERG-MARQUARDT REGULARIZATION FOR THE BACKWARD HEAT EQUATION WITH FRACTIONAL DERIVATIVE

被引：2

作者：

Pornsawad, Pornsarp ^{[1
,4
]}

Bockmann, Christine ^{[2
,3
]}

Panitsupakamon, Wannapa ^{[1
,4
]}

机构：

[1] Silpakom Univ, Fac Sci, Dept Math, 6 Rachamakka Nai Rd, Mueang Nakhon Pathom Dis 73000, Nakhon Pathom, Thailand

[2] Univ Potsdam, Inst Math, Karl Liebknecht Str 24-25, D-14476 Potsdam, Germany

[3] Alfred Wegener Inst, Helmholtz Ctr Polar & Marine Res, Telegrafenberg A45, D-14473 Potsdam, Germany

[4] Mahidol Univ, Ctr Excellence Math, Rama 6 Rd, Bangkok 10400, Thailand

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2022年 / 57卷

关键词：

  ill-posed problems; time-fractional derivative; backward heat problem; Levenberg-Marquardt method; a posteriori stopping rule; optimal order; RUNGE-KUTTA INTEGRATORS; ASYMPTOTICAL REGULARIZATION; INVERSE PROBLEMS;

D O I：

10.1553/etna_vol57s67

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The backward heat problem with time-fractional derivative in Caputo???s sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg???Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a H??lder-type source condition. Numerical examples for one and two dimensions are provided.

引用

页码：67 / 79

页数：13

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