Some observations on unsymmetric radial basis function collocation methods for convection–diffusion problems

In this paper, we re‐investigate the unsymmetric radial basis function (RBF) collocation method for solving convection–diffusion problems with high Péclet number as in Power and Barraco (Computers and Mathematics with Applications 2002; 43:551). By testing different RBFs and different numbers of nodes, we found that the unsymmetric method can still solve high Péclet number problems reasonably well by using more nodes and domain decomposition techniques. Compared to solving one large problem, the domain decomposition method is shown to be very efficient and can improve the accuracy especially when the Péclet number is not that high. From our tests, it seems that the RBFs r4 ln r and r8 ln r are not very stable, while r6 ln r, r5 and r7 perform very well. Copyright © 2003 John Wiley & Sons, Ltd.

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