A SECB Method For A Sideways Heat Equation And Fourier Method With A-posteriori Parameter Choice

In this theories,we consider a new a-priori constraint for a sideways heat equa-tion. Then this new constraint is used as a source condition for regularization resulting in a new computational method. An error estimate is obtained on this new regularization tcchnique,showing an improvement over the existing methods by the traditional a-priori constraint at the boundary reconstruction.Moreover,the Fourier method is a convenient regularization method for solving a class of ill-posed problems. This class of ill-posed problems can be also formulated as the problem of ill-posed multiplication operator equation in the frequency domain. We investigate the Fourier method within the framework of regularization theory thoroughly for solving the severely ill-posed problems. Many ill-posed examples are provided.