A mollification method for a Cauchy problem for the Helmholtz equation

ABSTRACTThe Cauchy problem for the Helmholtz equation is considered. This problem is severely ill-posed, that is, the solution does not depend continuously on the data. To solve the problem numerically a mollification method is proposed. Convergence on error estimates between the exact solution and its approximation are obtained. Some numerical examples are given to show that the method works effectively.