The method of fundamental solutions for solving a Cauchy problem of Laplace's equation in a multi-connected domain

In this article, the method of fundamental solutions is applied to solve a Cauchy problem of Laplace's equation in a multi-connected domain. This problem is severely ill-posed in the sense of Hadamard. To solve effectively the discrete ill-posed problem resulted from a boundary collocation scheme, Tikhonov regularization and L-curve choice for a regularization parameter have been used for determining a stable approximate solution. The feasibility and validity of the proposed approach is demonstrated through several numerical examples.