One Regularization Method For A Cauchy Problem Of The Modified Helmholtz Equation

The Cauchy problem for the modified Helmholtz equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Thus the regularization methods are required to recover the numerical stability. In this paper, we propose a modified non-local boundary value problem method to treat this ill-posed problem. Convergence estimates are obtained under a-priori bound assumptions for the exact solution and the selection of regularization pa-rameter. Some numerical results are given to show that this method is stable and feasible.