Local RBF-FD solutions for steady convection-diffusion problems

This paper describes the application of radial basis function (RBF) based finite difference type scheme (RBF-FD) for solving steady convection-diffusion equations. Numerical studies are made using multiquadric (MQ) RBF. By varying the shape parameter in MQ, the accuracy of the solution is seen to be highly improved for large values of Reynolds' numbers. The developed scheme has been compared with the corresponding finite difference scheme and found that the solutions obtained using the former are non-oscillatory. Copyright © 2007 John Wiley & Sons, Ltd.