Direct method for a Cauchy problem with application to a Tokamak

This note is concerned with a new direct (non-iterative) method for the solution of an elliptic inverse problem. This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition. Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations. Four examples are used to study the applicability of the method with the presence of noise.