On the numerical solution of direct and inverse problems for the heat equation in a semi-infinite region

We consider the initial boundary value problem for the heat equation in a region with infinite and finite boundaries (direct problem) and the related problem to reconstruct the finite boundary from Cauchy data on the infinite boundary (inverse problem). The numerical solution of the direct problem i...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 108; no. 1; pp. 41 - 55
Main Author: Chapko, Roman
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.08.1999
Elsevier
Subjects:
Collocation method
Exact sciences and technology
Green's function
Heat equation
Initial boundary value problem
Integral equation
Inverse boundary problem
Mathematical analysis
Mathematics
Newton method
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Regularization
Sciences and techniques of general use
Semi-infinite region
Trigonometric interpolation
Trigonometric interpolation
Initial boundary value problem
Heat equation
Semi-infinite region
Inverse boundary problem
Green's function
Integral equation
Collocation method
Newton method
Regularization
Sobolev space
Initial value problem
Green function
Uniqueness theorem
Partial differential equation
Convergence
Inverse problem
Direct problem
Interpolation
Boundary value problem
ISSN:0377-0427, 1879-1778
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Summary:We consider the initial boundary value problem for the heat equation in a region with infinite and finite boundaries (direct problem) and the related problem to reconstruct the finite boundary from Cauchy data on the infinite boundary (inverse problem). The numerical solution of the direct problem is realized by a boundary integral equation method. For an approximate solution of the inverse problem we use a regularized Newton method based on numerical approach for the direct problem. Numerical examples illustrating our results are presented.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(99)00099-0