The Research Of Meshfree Barycentric Interpolation Collocation Method In Some Partial Differential Equations

The barycentric interpolation collocation method is a high-precision numerical method,it is a collocation method based on differential equation.The approximation of unknown function is expressed as interpolation collocation at disperse nodes.Meshfree barycentric interpolation collocation method include two kinds,they are barycentric Lagrange interpolation collocation method and barycentric rational interpolation collocation method.In the past,mathematical researchers in China and abroad had did a lot of research about meshfree barycentric interpolation collocation method,but in their research,using this method to solve partial differential equations and equation sets are very little.Because this method comes from engineering,there are no theoretical analysis of this method in solving differential equation.So,in this paper,we'll start from this,apply meshfree barycentric interpolation collocation method in KdV equation,KdV-Burgers equation and singularly perturbed delay partial differential equations.In the same way,we'll break through the theoretical analysis,include astringency and stability.The emphasis of this paper is applying meshfree barycentric interpolation collocation method in KdV equation,KdV-Burgers equation and singularly perturbed delay partial differential equations,break through the theoretical analysis.With some examples,this paper will discuss the accuracy and calculate of meshfree barycentric interpolation collocation method.The first chapter introduces the development of meshfree barycentric interpolation collocation method,expound the status and meaning of researching this method.The second chapter introduces the specific steps about using this method to solve differential equations,the infliction of boundary conditions and direct linear iteration method.The third chapter introduces using the meshfree barycentric interpolation collocation method to solve KdV equation,KdV-Burgers equation and singularly perturbed delay partial differential equations.The fourth chapter discuss about the theoretical analysis of barycentric interpolation collocation method,include astringency and stability.The fifth chapter summarizes all the content of this paper,and puts forward some improved suggestion to study the method for the future.