Two Regularization Strategies For Solving A Cauchy Problem Of The Modified Helmholtz Equation

In this paper,we consider a Cauchy problem of the modified Helmholtz equation.It's a severely ill-posed problem.We propose a mollification method and fractional tikhonov method to obtain the stable numerical solutions for this problem,respectively.Then the estimate between regularization approximation solution and exact solution are given.Finally several examples are provided to illustrate the effectiveness of the two regularization methods.