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In this paper a simple and convenient new regularization method for solving backward heat equation— Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.
We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective .
We introduce a central difference method for a backward heat conduction problem (BHCP). Error estimates for this method are provided together with a selection rule for the regularization parameter (the space step length). A numerical experiment is presented in order to illustrate the role of the regularization parameter.