On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation.

In this paper, we consider the modified inhomogeneous Helmholtz equation Δ u( x, y) u( x, y) f( x, y), x , 0 y 1, with inhomogeneous Cauchy data being given at y 0. The problem is known to be ill-posed, as the solution (if exists) does not depend continuously on the given data. We propose a regularization method to obtain a stable approximate solution of the problem and get some error estimates. Finally, a numerical example shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]