A numerical method for backward parabolic problems with non-selfadjoint elliptic operators

DOI10.1016/S0168-9274(00)00025-8zbMath0976.65080MaRDI QIDQ5932816

Alemdar Hasanov, Jennifer L. Mueller

Publication date: 19 December 2001

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

zbMATH Keywords

stabilityconvection-diffusion equationbackward parabolic problemmodified alternating direction schemequasi-solution

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for second-order parabolic equations (35K15)

Related Items (22)

Inverse heat conduction problems with boundary and final time measured output data ⋮ A regularized optimization method for identifying the space-dependent source and the initial value simultaneously in a parabolic equation ⋮ Comparative numerical analysis of identification problems related to nonlinear transport-diffusion model of a settler ⋮ Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: weak solution approach ⋮ A regularization of the backward problem for nonlinear parabolic equation with time-dependent coefficient ⋮ A numerical solution for a quasi solution of the time-fractional stochastic backward parabolic equation ⋮ Numerical identification of initial temperatures in heat equation with dynamic boundary conditions ⋮ A modified integral equation method of the semilinear backward heat problem ⋮ Determination of the unknown Cauchy data in a linear parabolic problem from the measured data at the final time ⋮ Solution of the backward problem for the space-time fractional diffusion equation related to the release history of a groundwater contaminant ⋮ A comparative study on applying the method of fundamental solutions to the backward heat conduction problem ⋮ A variational approach to reconstruction of an initial tsunami source perturbation ⋮ Recovering the spatial distribution of a groundwater contaminant at a prior time: the forward collocation method ⋮ An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation ⋮ Hölder stability for a class of initial inverse nonlinear heat problem in multiple dimension ⋮ Numerical algorithms for a sideways parabolic problem with variable coefficients ⋮ Quasi solution of a backward space fractional diffusion equation ⋮ Two dimensional determination of source terms in linear parabolic equation from the final overdetermination ⋮ Simultaneous identification and reconstruction of the space-dependent reaction coefficient and source term ⋮ A quasi solution for a nonlinear inverse stochastic partial differential equation of parabolic type ⋮ A numerical method for determining a quasi solution of a backward time-fractional diffusion equation ⋮ Identification of the pollution source from one-dimensional parabolic equation models

Uses Software

• Regularization tools
• UTV

Cites Work

• Numerical solution of the equation of heat conduction for preceding times
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Limitations of the \(L\)-curve method in ill-posed problems
• Some backward uniqueness results
• Time Discretization in the Backward Solution of Parabolic Equations. I
• Time Discretization in the Backward Solution of Parabolic Equations. II
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Stability theory of difference schemes and iterative methods
• Rank-Deficient and Discrete Ill-Posed Problems
• A Kernel-based Method for the Approximate Solution of Backward Parabolic Problems
• Non-convergence of the L-curve regularization parameter selection method
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A numerical method for backward parabolic problems with non-selfadjoint elliptic operators