Regularization of backward heat conduction problem

We study the backward heat conduction problem in an unbounded region. The problem is ill-posed, in the sense that the solution if it exists, does not depend continuously on the data. Continuous dependence of the data is restored by cutting-off high frequencies in Fourier domain. The cut-off parameter acts as a regularization parameter. The discrepancy principle, for choosing the regularization parameter and double exponential transformation methods for numerical implementation of regularization method have been used. An example is presented to illustrate applicability and accuracy of the proposed method.

► The introduced method is simply applicable to approximate solution at t = 0 which is self starting.
► The error estimated is independent of t and the norm of exact solution.
► The discrepancy principle, for choosing the regularization parameter and double exponential transformation methods have been used.