We present a non-overlapping domain decomposition Method (DDM) applied to the method of fundamental solution (MFS) to treat the non-linear poisson-type equations. The MFS often deals with the linear and non-linear poisson's equations by approximating a particular solution via employing radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. In the current work, the domain is divided into two subdomains and the MFS is applied to each subdomain followed by assembling the equations in a sparse linear system. The conditioning of the interpolation matrix and the computational efficiency are improved due to reducing the size of the subproblems. The numerical examples illustrate the effectiveness of the presented method.
