Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation

DOI10.1016/j.cam.2014.11.026zbMath1306.65260OpenAlexW1974058933MaRDI QIDQ482695

Yu-Bin Zhou, Ting Wei, Jun-Gang Wang

Publication date: 6 January 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.11.026

zbMATH Keywords

convergenceinverse problemill-posed problemoptimal error boundfractional diffusion equationa posteriori parameter choicesimplified Tikhonov regularization method

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) Fractional partial differential equations (35R11)

Related Items (21)

Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method ⋮ On a backward problem for nonlinear time fractional wave equations ⋮ A Tikhonov regularization method for solving a backward time-space fractional diffusion problem ⋮ Two regularization methods for identifying the source term problem on the time-fractional diffusion equation with a hyper-Bessel operator ⋮ Filter regularization for final value fractional diffusion problem with deterministic and random noise ⋮ Regularization of backward time-fractional parabolic equations by Sobolev-type equations ⋮ Optimal error bound and truncation regularization method for a backward time-fractional diffusion problem in Hilbert scales ⋮ On Tikhonov's method and optimal error bound for inverse source problem for a time-fractional diffusion equation ⋮ Regularization of a backward problem for composite fractional relaxation equations ⋮ A generalized quasi‐boundary value method for the backward semi‐linear time‐fractional heat problem in a cylinder ⋮ Two regularization methods for identifying the source term of Caputo–Hadamard time‐fractional diffusion equation ⋮ On a backward problem for inhomogeneous time-fractional diffusion equations ⋮ On a time-space fractional backward diffusion problem with inexact orders ⋮ A fractional Landweber method for solving backward time-fractional diffusion problem ⋮ Regularization and error estimates for an inverse heat problem under the conformable derivative ⋮ On a backward problem for nonlinear fractional diffusion equations ⋮ Optimal regularization for an unknown source of space-fractional diffusion equation ⋮ Backward problem for time-space fractional diffusion equations in Hilbert scales ⋮ Recovering the historical distribution for nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity in higher dimensional space ⋮ Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework ⋮ Stability results for backward time-fractional parabolic equations

Uses Software

• Matlab
• Mittag-Leffler
• mlf

Cites Work

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