An improved non-local boundary value problem method for a Cauchy problem of the Laplace equation (Q663485)

This article deals with a Cauchy problem for the Laplace equation in a rectangle, with the solution that can be obtained by solving two Cauchy problems for Laplace equation. Such problems arise from many real applications, such as non destructive testing techniques, geophysics, cardiology, etc. The authors propose an improved non-local boundary value problem method in order to construct stable approximate solutions for the two Cauchy problems. Convergence and stability estimates are obtained under some \textit{a~ priori} bound assumptions for the exact solution. Some numerical examples show that the proposed regularization method is effective and stable.