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Zbl 1166.65048
Feng, Xiao-Li; Qian, Zhi; Fu, Chu-Li
Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region. (English)
[J] Math. Comput. Simul. 79, No. 2, 177-188 (2008). ISSN 0378-4754

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.
[Rolf Dieter Grigorieff (Berlin)]

MSC 2000:: *65M30 Improperly posed problems (IVP of PDE, numerical methods)
35K05 Heat equation
35R25 Improperly posed problems for PDE
65M70 Spectral, collocation and related methods (IVP of PDE)

Keywords: backward heat conduction; ill-posed problem; Fourier method; Tikhonov regularization; error estimate; numerical experiments

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