Radial Basis Method For Convection Diffusion Equation

This paper studies Radial Basis Collocation Method, which is a truly mesh less method. Based on this, it applies this method to solving linear convection diffusion equation especially nonlinear convection diffusion equation. There are four chapters. The first chapter introduces the background of the Radial Basis Collocation. The second chapter is preliminary of knowledge. Firstly, we review an important and basic method of numerically solving partial differential equation—Collocation Method. Secondly, the Radial Basis Function Approximation is given. In chapter three, we apply RBC to solve the 1D and 2D linear convection diffusion equation especially nonlinear equation. Further, it gives the algorithm of this model in this paper, and checks the experiment result through calculating on computer. Numerical studies show that the method improves the approximation significantly. In the last chapter, it recount summary and forecast of RBC.