A meshless method for solving nonhomogeneous Cauchy problems ?
In this paper the method of fundamental solutions (MFS) and the method of particular solution (MPS) are combined as a one-stage approach to solve the Cauchy problem for Poisson's equation. The main idea is to approximate the solution of Poisson's equation using a linear combination of fundamental solutions and radial basis functions. As a result, we provide a direct and effective meshless method for solving inverse problems with inhomogeneous terms. Numerical results in 2D and 3D show that our proposed method is effective for Cauchy problems.
meshless methods cauchy problem method of fundamental solutions the method of particular solutions radial basis functions inverse problem tikhonov's regularization