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
收藏
页码：67 / 79
页数：13
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