An a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems

Zhang, Yuanxiang; Fu, Chu-Li; Ma, Yongxin

doi:10.1016/j.cam.2013.04.046

Cited by 9 publications

(4 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, we put the definition of f n into (17). It is easy to see that Equation (1) becomes the following operator equation…”

Section: Ill-posed Analysis and Conditional Stabilitymentioning

confidence: 99%

“…In an environment with an increasing energy shortage, source term identification helps to find new energy. A variety of regularization methods are proposed by scholars to deal with inverse problems, which include, for example, the Tikhonov regularization method [8,9], Fourier regularization method [10,11], Quasi-boundary value regularization method [12,13], Quasi-reversibility regularization method [14,15], truncation regularization method [16,17], Landweber iterative regularization method [18,19], etc. This paper will use the Tikhonov regularization method and Quasi-boundary regularization method to deal with the problem of source term identification.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

Zhang,

Yang,

2024

Mathematics

View full text Add to dashboard Cite

In this paper, we delve into the challenge of identifying an unknown source in a space-time fractional diffusion-wave equation. Through an analysis of the exact solution, it becomes evident that the problem is ill-posed. To address this, we employ both the Tikhonov regularization method and the Quasi-boundary regularization method, aiming to restore the stability of the solution. By adhering to both a priori and a posteriori regularization parameter choice rules, we derive error estimates that quantify the discrepancies between the regularization solutions and the exact solution. Finally, we present numerical examples to illustrate the effectiveness and stability of the proposed methods.

show abstract

“…Now, we put the definition of f n into (17). It is easy to see that Equation (1) becomes the following operator equation…”

Section: Ill-posed Analysis and Conditional Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

Zhang,

Yang,

2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…The nonhomogeneous case of the BHCP has been considered by Trong et al [28,29]. By using a truncation regularization method, the one dimensional case of the BHCP with the time-dependent diffusion coefficient has been formulated in [30][31][32]. A modified quasi-reversibility method for the n-dimensional BHCP has been also developed in [33].…”

Section: Introductionmentioning

confidence: 99%

On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

Karimi

Moradlou

Hajipour

2018

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

In this work, an accurate regularization technique based on the Meyer wavelet method is developed to solve the ill-posed backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". In principle, the extremely ill-posedness of the considered problem is caused by the amplified infinitely growth in the frequency components which lead to a blow-up in the representation of the solution. Using the Meyer wavelet technique, some new stable estimates are proposed in the Hölder and Logarithmic types which are optimal in the sense of given by Tautenhahn. The stability and convergence rate of the proposed regularization technique are proved. The good performance and the high-accuracy of this technique is demonstrated through various one and two dimensional examples. Numerical simulations and some comparative results are presented.

show abstract

“…In [22,23], the authors used the truncation method to solve BHCP. In [24][25][26], the authors used the truncation method to solve a cauchy problem for the Helmholtz equation and the modified Helmholtz equation.…”

Section: Introductionmentioning

confidence: 99%

The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain

Yang

Sun

et al. 2018

Bound Value Probl

View full text Add to dashboard Cite

In this paper, identifying the initial value for high dimension heat equation with inhomogeneous source on a spherical symmetric domain is investigated. The truncation regularization method is a powerful technique for solving this inverse problem. We prove the convergence estimates between the regularization solution and the exact solution under the prior and the posterior regularization parameter choice rulers. A numerical example is presented to validate the effectiveness of this method.

show abstract

An a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems

Cited by 9 publications

References 36 publications

Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain

Contact Info

Product

Resources

About