We present a non-overlapping domain decomposition method (DDM) for the method of fundamental solution (MFS) to improve the conditioning of the problem \cite{kamal}. This method often deal with the Poisson-type equations by approximating a particular solution via radial basis functions (RBF). When imposing the Numann boundary condition, the use of osculatory RBF (ORBF) has a considerable effect on the accuracy. In the case of employing a non-overlapping DDM with an interface boundary, the physical matching conditions including a Nummann type are essentially applied. Therefore, the use of ORBF can improve the quality of the solution.
