Analysis on the upwind local radial basis functions method to solve convection dominated problems and it's application for MHD flow

摘要

Ill-conditioning is drawback of global radial basis functions (RBFs) method. Local RBFs method has overcome this difficulty and has become popular as an alternative methodology. In this paper, we analyze local RBFs method to solve singularly perturbed linear convection-diffusion problems. In some articles, it is investigated numerically but our aim is mainly to prove stability, consistency and convergence of local RBF method for boundary layer problems. It is known that the approximate error bound of Local RBFs method depends on two factors, Local density of knots, h, and the shape parameter, c. It is proven that this method is first order consistent. for verification, an unsteady Magnetohydrodynamic (MHD) free convective heat and mass transfer flow with Thermophoresis past a radiate inclined permeable plate in the presence of variable chemical reaction and temperature dependent viscosity is considered. Additionally some mathematical test problems are approximated. Numerical results reveal that the proposed method is accurate than upwind finite difference method. The optimal shape parameter strategy will also be utilized to approximate significant solutions.