Abstract
The Auxiliary Source Method, (ASP), Cekirge and Lehr, is extended for the solution of inhomogenous and nonlinear elliptic equations. A set of localized internal functions (LIFT) Brebbia is added to the functions of the ASP method to take care of the inhomogeneous part of the elliptic partial differential equation. Since the solution of the inhomogeneous equation is simplified to a great extent, an iteration technique for nonlinear cases is included. An example for the inhomogenous solution is presented to illustrate the method in the paper.