Barycentric Interpolation Collocation Method For Some Evolution Equations (Groups)

The meshless method is a collocation method that needs neither a initial mesh generation nor the grid reconstruction.It is a method that depends on the differential equations of the strong form,which ensures the high accuracy and reduces the computing complexity numerical calculation method.Its essence is to combine the use of barycentric interpolation to approximate function with collocation method to solve the problem.Before that,some professionals applied the meshless barycentric interpolation collocation method to make a lot of research.However,the application of this method to evolution equations(groups)is very rare.The key point of this paper is to apply meshless barycentric interpolation collocation method to some evolution equations(groups),and to study the practical application of evolution equations interpolation collocation method.Through the cooperation with numerical examples,the article will illustrate the meshless barycentric interpolation collocation method both accuracy and efficiency is higher than other numerical methods.In the first chapter,introduction of the development situation of topic and meshless barycenter interpolation collocation method will be given,which makes the specific research content of the article clearly.In the second chapter,the meshless barycentric interpolation collocation method is introduced.The main points are: interpolation method,differential matrix form,initial boundary condition application and direct linear iteration method.In the third chapter,the meshless barycentric interpolation collocation method is applied to the long wave equation(RLW),and a numerical results is used to illustrate the superiority of the method.The fourth chapter,the meshless barycentric interpolation collocation method is applied to the KdV equation,Schr(?)dinger-KdV equation,Boussinesq system,and numerical examples shows that the combination of this method can be used to solve some evolution equations groups,and the calculation result is well.The fifth chapter,the meshless barycentric interpolation collocation method is applied to simulate the fixed assets model,which shows that the method has good application in economic problems.The sixth chapter,summarize the content of this study,and put forward some suggestions and ideas for the further research of this method.