Meshfree Collocation Methods For Three Kinds Of Nonlinear Reaction Diffusion Equations

Many mathematical models of biology, physics and chemistry in nature can be represented by differential equations, but most of differential equations' exact solu-tions can't be found. With the swift development of Computer technology, We can figured out the numerical solution of differential equations by computer and simulate natural phenomenon. Meshfree method is a rapid development new numerical method in recent years. Compared with the traditional finite element method and finite differ-ence methods, it is with an arbitrary take fixed coordinates tectonic interpolation basis function discrete partial differential equation, partially or completely mesh dissection, This makes it easy to simulate many complex natural phenomenon. At present,it has become an important approach for solving partial differential equations.This paper performs a meshfree collocation method based on the interpolation of radial basis functions(RBFs) for solving the nonlinear reaction-diffusion equa-tions.These problems concern generalized Fisher equation, Allen-Cahn equation and Nonlinear singular reaction-diffusion equations. A nonlinear problem is changed into a linear one via this method. Compared with the traditional finite element method and finite differential method, the new algorithm in this paper doesn't need any mesh and it is simple and vivid to extend hign-dimensional problems. Some numerical results and simulations are also presented to demonstrate the effectiveness of the method.