An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data

YUAN Xiaoyu; FENG Xiaoli; ZHANG Yun

doi:10.21656/1000-0887.440066

Volume 44 Issue 10

Oct. 2023

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YUAN Xiaoyu, FENG Xiaoli, ZHANG Yun. An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data[J]. Applied Mathematics and Mechanics, 2023, 44(10): 1260-1271. doi: 10.21656/1000-0887.440066

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An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data

doi: 10.21656/1000-0887.440066

School of Mathematics and Statistics, Xidian University, Xi'an 710126, P.R.China

Received Date: 2023-03-14
Rev Recd Date: 2023-05-05
Publish Date: 2023-10-31

Abstract

Abstract

The backward problem of space-fractional diffusion equations with perturbed diffusion coefficients and perturbed final data was considered. The initial data were recovered from the measured data at the final time. Given the severe ill-posedness of this problem, an iterative regularization method was proposed to tackle it. The convergence error estimate between the exact and approximate solutions was obtained under the assumption of an a-priori bound on the exact solution. Finally, several numerical simulations were conducted to verify the effectiveness of this method.
- space-fractional diffusion equation,
- backward problem,
- ill-posedness,
- iterative regularization method

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References

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