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

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In this paper we present a method
based on using Exponential Basis Functions (EBFs) to solve a class of two-dimensional
time dependent engineering problems. 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
can be 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 problems such as transient heat conduction and wave propagation in
solids. Several problems are solved to show the capabilities of the approach
used.

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http://www.sciencedirect.com/science/article/pii/S0021999113000776