A comparative analysis of numerical methods of solving the continuation problem for 1D parabolic equation with the data given on the part of the boundary

DOI10.1007/s10444-018-9631-7zbMath1415.65215OpenAlexW2893137895MaRDI QIDQ2000494

Dmitriy V. Klyuchinskiy, Andrey Belonosov, Maxim A. Shishlenin

Publication date: 28 June 2019

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-018-9631-7

zbMATH Keywords

singular value decompositionnumerical methodsparabolic equationgradient methodcontinuation problemfinite-difference scheme inversion

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems in optimal control (49N45)

Related Items (5)

CPU-time and RAM memory optimization for solving dynamic inverse problems using gradient-based approach ⋮ Features of numerical reconstruction of a boundary condition in an inverse problem for a reaction-diffusion-advection equation with data on the position of a reaction front ⋮ On the features of numerical solution of coefficient inverse problems for nonlinear equations of the reaction-diffusion-advection type with data of various types ⋮ The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method ⋮ Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
• Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems
• Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs
• Inverse and ill-posed problems. Theory and applications.
• Comparative analysis of methods for regularizing an initial boundary value problem for the Helmholtz equation
• Carleman estimates for the regularization of ill-posed Cauchy problems
• Numerical analysis of an energy-like minimization method to solve a parabolic Cauchy problem with noisy data
• Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
• Iterative methods for an inverse heat conduction problem
• Regularization of the continuation problem for elliptic equations
• Inverse problems for the ground penetrating radar
• Quasi-solution in inverse coefficient problems
• Wavelet and Fourier Methods for Solving the Sideways Heat Equation
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• Optimizational method for solving the Cauchy problem for an elliptic equation
• Numerical solution of the sideways heat equation by difference approximation in time
• Regularization Methods of the Continuation Problem for the Parabolic Equation
• An alternating iterative procedure for the Cauchy problem for the Helmholtz equation

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