A Discretized Tikhonov Regularization Method for a Fractional Backward Heat Conduction Problem

Abstract EN

We propose a numerical reconstruction method for solving a time-fractional backward heat conduction problem.

Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurements of transient temperature at a fixed final time.

The standard Tikhonov regularization technique using the norm of reproducing the kernel Hilbert space as the penalty term is adopted to provide a stable solution when the measurement data contains noise.

Numerical results indicate that the proposed method is efficient.