The mollification method and the numerical solution of the inverse heat conduction problem by finite differences

DOI10.1016/0898-1221(89)90022-9zbMath0677.65122OpenAlexW2073556365MaRDI QIDQ1123573

Diego A. Murio

Publication date: 1989

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(89)90022-9

zbMATH Keywords

numerical examplefinite differenceinverse heat conduction problemmollification methodimproperly posed

Mathematics Subject Classification ID

Heat equation (35K05) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Applications to the sciences (65Z05)

Related Items (15)

Graphical representations for the successive Lorentz transformations. Application: Lorentz contraction and its dependence on Thomas rotation ⋮ The space marching solution of the inverse heat conduction problem and the identification of the initial temperature distribution ⋮ Identification of transmissivity coefficients by mollification techniques. II: \(n\)-dimensional elliptic problems ⋮ Reconstruction of inaccessible boundary value in a sideways parabolic problem with variable coefficients -- forward collocation with finite integration method ⋮ Complex boosts: a Hermitian Clifford algebra approach ⋮ Regularization of the inverse Laplace transform by mollification ⋮ A mollified space marching finite differences algorithm for the inverse heat conduction problem with slab symmetry ⋮ A stable space marching finite differences algorithm for the inverse heat conduction problem with no initial filtering procedure ⋮ Unnamed Item ⋮ Identifying an unknown source term in a heat equation with time-dependent coefficients ⋮ A spring-damping regularization of the Fourier sine series solution to the inverse Cauchy problem for a 3D sideways heat equation ⋮ Numerical identification of interface source functions in heat transfer problems under nonlinear boundary conditions ⋮ Solution of inverse heat conduction problems with phase changes by the mollification method ⋮ Identifying an unknown source term in a time-space fractional parabolic equation ⋮ Numerical algorithms for a sideways parabolic problem with variable coefficients

Cites Work

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• Estimates and reglarization for solutions of some ill-posed problems of elliptic and parabolic type
• An integral solution for the inverse heat conduction problem after the method of Weber
• Parameter selection by discrete mollification and the numerical solution of the inverse heat conduction problem
• Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side
• Analysis and solution of the ill-posed inverse heat conduction problem
• A Stable Approach to Solving One-Dimensional Inverse Problems
• The Mollification Method and the Numerical Solution of an Inverse Heat Conduction Problem
• Determining Surface Temperatures from Interior Observations
• The Inverse Problem in Transient Heat Conduction
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems

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