Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region

DOI10.1016/j.matcom.2007.11.005zbMath1166.65048OpenAlexW2084312350MaRDI QIDQ955285

Chu-Li Fu, Zhi Qian, Xiao-Li Feng

Publication date: 19 November 2008

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2007.11.005

zbMATH Keywords

numerical experimentserror estimateTikhonov regularizationill-posed problemFourier methodbackward heat conduction

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (13)

Identification of the initial condition in backward problem with nonlinear diffusion and reaction ⋮ A regularization of the backward problem for nonlinear parabolic equation with time-dependent coefficient ⋮ A modified integral equation method of the semilinear backward heat problem ⋮ A meshless method based on RBFs method for nonhomogeneous backward heat conduction problem ⋮ Some extended results on a nonlinear ill-posed heat equation and remarks on a general case of nonlinear terms ⋮ Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation ⋮ On an inverse problem for fractional evolution equation ⋮ Two regularization methods for backward heat problems with new error estimates ⋮ Some filter regularization methods for a backward heat conduction problem ⋮ Hölder stability for a class of initial inverse nonlinear heat problem in multiple dimension ⋮ Regularized solution of an inverse source problem for a time fractional diffusion equation ⋮ An improved regularization method for initial inverse problem in 2-D heat equation ⋮ Stability and regularization of a backward parabolic PDE with variable coefficients

Cites Work

• A mollification method for ill-posed problems
• The boundary element method for the solution of the backward heat conduction equation
• Stability of the solution of backward heat equation on a weak compactum
• A stability estimate on the regularized solution of the backward heat equation.
• Solution of inverse diffusion problems by operator-splitting methods
• On optimal regularization methods for the backward heat equation
• Group preserving scheme for backward heat conduction problems
• On stable numerical differentiation
• An introduction to the mathematical theory of inverse problems
• An iterative boundary element method for solving the one-dimensional backward heat conduction problem
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