MODIFIED LAVRENTIEV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF HELMHOLTZ-TYPE EQUATION

In this paper, a Cauchy problem of Helmholtz-type equation with nonhomogeneous Dirichlet and Neumann datum is researched. We establish the result of conditional stability under an a-priori assumption for exact solution. A modified Lavrentiev regularization method is used to overcome its ill-posedness, and under an a-priori and an a-posteriori selection rule for the regularization parameter we obtain the convergence result for the regularized solution, the corresponding results of numerical experiments verify that the proposed method is stable and workable, this work is an extension on the related research results of existing literature in the aspect of regularization theory and algorithm for Cauchy problem of Helmholtz-type equation.