The main purpose of this study is to provide two efficient numerical methods for solving time-dependent differential equations. In the first one, the governing differential equation was exactly satisfied by the appropriate selection of Exponential basis functions (EBFs). The initial and the boundary conditions are simultaneously satisfied through a collocation technique. The ability in solution of both direct and inverse problems, with justify; LINE-HEIGHT: normal; TEXT-INDENT: 11.35pt; MARGIN: 0in 0in 0pt" The second method employs EBFs in a novel approach using pre-integration relations between acceleration, velocity and displacement fields. In this method, the initial conditions are exactly satisfied in a time marching manner. The equilibrium equation is satisfied using a time-weighted residual method. A collocation technique is also used for implementation of boundary conditions at the end of each time step. The ability to speed up calculations and modeling problems in infinite domains are two important features of this method. Key Words: Meshless Method, Time dependent problems, Exponential Basis Functions, Collocation, Time Weighted Residual Method.
