The Application Of Meshless Radial Basis Functiion Interpolation Method In The Calculation Of Partial Differential Equation

Meshless method is a promising numerical method following the traditional numerical methods such as finite difference method and finite element method.Compared with the traditional numerical method,because of independence on grid,strong adaptability etc.With the research of scholars at home and abroad in recent years,meshless methods are becoming more and more mature and diverse.Based on radial basis function(),meshless method having the advantages of simple form and high numerical precision becomes increasingly one of the hot topics in recent years.In the paper,we first introduced the interpolation,respectively simulating two numerical experiments consisting of high-order derivative interpolation and multiple integral interpolation,and the range of shape parameter c was given.The result of numerical experiments showed that the multiple integral interpolation is more stable and accurate than the high-order derivative interpolation,and the choice of shape parameter c is more flexible.The numerical schemes of derivative interpolation and integral interpolation for ordinary differential equations were given.In the global derivative interpolation method,due to strong singularity of coefficient matrix,the researchers proposed a local interpolation method,and given the upwind scheme to improve the stability of numerical solution,we analyzed and compared the effects of global and local derivative interpolation method for numerical experiments.In addition,the error estimation of radial basis interpolation finite integral method was given in combination with Tikhonov regularization method.The estimation indicated that the higher smoothness of the function,the higher numerical accuracy.Numerical experiment demonstrated that the finite integration method which combined with interpolation had the characteristics of high numerical precision,simple structure and flexible selection of shape parameter c.