Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation

The inverse heat conduction problem (IHCP) can be considered to be a sideways parabolic equation in the quarter plane, and now the results available in the literature on IHCP mainly devoted to the standard sideways heat equation. Numerical methods have been developed also for more general equations, but, in most cases, the stability theory and convergence proofs have not been generalized accordingly. This paper remedies this by a simplified Tikhonov and a new Fourier regularization methods on a general sideways parabolic equation. Some known results for sideways heat equation are only the special case of the conclusions in this paper.The numerical example shows that the computation effect is satisfactory.