Semi-discretization Difference Approximation For A Cauchy Problem Of Heat Equation In Two-dimensional Space

in this paper,we consider a non-characteristic Cauchy problem of heat equation in two-dimensional setting and differential regularization method.It is different from the general regularization theory which was proposed by Engl, Hanke and Neubauer. According to the instability of ill-posed problem,we should conduct a regularization method for this problem,so the paper's main work was to apply a semi-discretization difference approximation to establish the regularized solution.In certain priori assumptions,we can get an optimal error estimation with the appropriate regularization parameter h and k,And the regularization method has obtained the better convergence.Numerical examples show that the proposed method works effectively.