The fundamental solution of the eigenvalue equation for non-homogeneous time dependent partial differential equations

In this article, we present a boundary meshless method to solve non-homogeneous transient heat conduction problems. The method is based on using the time-dependent method of fundamental solution (MFS) for the homogeneous part and approximating a particular solution for the non-homogeneous part. The particular solution is approximated by the use of the fundamental solution of the associated eigenvalue equations. The nal linear system of equation is an ill-conditined problem. To avoid this difficulty, a singular decomposition method is employed. Some numerical results will be presented to demonstrate the effectiveness of the proposed method.Heat conduction problems, Boundary meshless method, Time-dependent fundamental solution.