LAUSR

Abstract The paper is considered a Cauchy problem for Helmholtz equation with mixed boundary in three-dimensional case. The problem is severely ill-posed (small deviation in the data may produce large errors in the computed solution), to solve this problem, a mollification method based on modified bivariate de la Vallee Poussin operator is proposed. The stable error estimates are obtained in Sobolev space under the suitable choice of mollification parameters and the a priori bounds assumption, the major approach to obtain the convergence estimates is to divide the real plane R 2 into 25 regions. The numerical experiments support the feasible, stable and convergent of our algorithm.