A Note on Wavelet and Fourier Methods for Solving the Sideways Heat Equation

We consider an inverse heat conduction problem (IHCP), the sideways heat equation. The problem is ill-posed: a small perturbation in the data may cause dramatically large error in the solution. In reference [1] theory analysis and numerical implementation are not consistent. We solve this inconsistence by proposing a new regularization method. The method not only has the same accurate and computing cost but also keeps parts of high-frequency components of the data compared to the results in [1].