A DELTA-SHAPED BASIS METHOD FOR ILL-POSED NONHOMOGENEOUS ELLIPTIC BOUNDARY VALUE PROBLEMS

In this paper, a Delta-shaped basis method is coupled with the method of fundamental solutions and Tikhonov regularization for solving ill-posed nonhomogeneous elliptic boundary value problems. Delta-shaped basis functions are used to approximate the source function since they can effectively handle scattered data and give rapidly convergent approximation. This approach also results in an easy derivation of a particular solution for a general type elliptic operator. The associated homogeneous problem is solved by the method of fundamental solutions with Tikhonov regularization. The approach is mesh free and is effective for domains of irregular shapes. Numerical results show that this method is accurate and stable against perturbed data.