Exponential basis functions in space and time: A meshless method for 2D time dependent problems

In this paper we present a method based on using exponential basis functions (EBFs) to solve well-known two-dimensional time dependent engineering problems such as elasto-dynamic ones. The formulation has much in common with those in three dimensional problems while time is taken as the third axis. The solution is first approximated by a summation of EBFs and then completed by satisfying the time dependent boundary conditions as well as the initial conditions through a collocation method. This is performed by considering a series of spatial and time dependent boundary points to satisfy the boundary conditions through a mixed collocation method. The solution method is presented in a time marching form which is capable of solving variety of problems such as transient heat conduction and wave propagation in solids. Several problems are solved to demonstrate the capabilities of the method.