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Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region. (English) Zbl 1166.65048
The authors consider the backward problem for the 1D heat equation with constant coefficients subject to homogeneous Dirichlet boundary conditions. The numerical method is based on the explicit solution of the forward problem which can be obtained by the Fourier method, i.e., the method of separation of variables. As approximate inverse the inverse of a truncated Fourier series is used which is regularized with the Tikhonov method. An error estimate for perturbed data is given as well as various numerical examples.

65M30Improperly posed problems (IVP of PDE, numerical methods)
35K05Heat equation
35R25Improperly posed problems for PDE
65M70Spectral, collocation and related methods (IVP of PDE)
Full Text: DOI
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