Two stable methods with numerical experiments for solving the backward heat equation

DOI10.1016/j.apnum.2010.09.006zbMath1206.65227OpenAlexW1979625656MaRDI QIDQ617641

Fabien Ternat, Oscar Orellana, Prabir K. Daripa

Publication date: 21 January 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.09.006

zbMATH Keywords

inverse problemregularizationnumerical examplesnumerical experimentsfilteringdispersion relationill-posed problemCrank-Nicolson methodEuler schemebackward heat equation

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for ill-posed problems for integral equations (65R30) 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)

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Stable backward diffusion models that minimise convex energies ⋮ On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor ⋮ Solving a backward heat conduction problem by variational method ⋮ Total variation regularization for the reconstruction of a mountain topography ⋮ Compact filtering as a regularization technique for a backward heat conduction problem ⋮ On an inverse problem: recovery of non-smooth solutions to backward heat equation ⋮ Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework ⋮ Application of the cut-off projection to solve a backward heat conduction problem in a two-slab composite system ⋮ An improved regularization method for initial inverse problem in 2-D heat equation ⋮ A regularization method for solving the radially symmetric backward heat conduction problem

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