Chinchapatnam, P.P., Djidjeli, K and Nair, P.B.
Unsymmetric and symmetric meshless schemes for
the unsteady convection–diffusion equation
Computer Methods in Applied Mechanics and Engineering, 195, (19-22), . (doi:10.1016/j.cma.2005.05.015).
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In this paper we investigate the application of unsymmetric and symmetric meshless collocation techniques with
radial basis functions for solving the unsteady convection–diffusion equation. We employ the method of lines approach
to discretize the governing operator equation. The stability of both explicit and implicit time-stepping schemes are analyzed.
Numerical results are presented for 1D and 2D problems to compare the performance of the unsymmetric and
symmetric collocation techniques. We compare the performance of various globally supported radial basis functions
such as multiquadric, inverse multiquadric, Gaussian, thin plate splines and quintics. Numerical studies suggest that
symmetric collocation is only marginally better than the unsymmetric approach. Further, it appears that both collocation
techniques require a very dense set of collocation points in order to achieve accurate results for high Pe´clet
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