Using Radial Basis Function (rbf) Numerical Solution Of Differential Equation Of The Fixed Point Algorithm Research And Application

Based on radial basis function’good capability of approximation, since1980s, peo-ple have began to use the radial basis function for the numerical solutions of partial differential equations(PDE),that is the meshless radial basis function method.In1990s Wu et al. applied one kind of radial basis function called MQ quasi-interpolation to solve PDEs. Considering the superiority of MQ quasi-interpolation in the freedom of node selection, Wu apply the MQ quasi-interpolation for adaptive methods of partial differential equations. Based on this, we give some moving knots equations in the thesis.An introduction to the main work and prior knowledge of this article is given in the first two chapters. In chapter3we analyze the4kinds of moving mesh partial differential equations (MMPDEs) proposed by Huang. Based on the analysis we give several new MMPDEs that performs better. Then a dynamical moving knots equation that considering both spatially and temporally combined with the MQ quasi-interpolation is given in chapter4. We give the algorithm and the error estimation. Numerical results show that our method can handle more steep turbulence.Since MQ quasi-interpolation performs well in numerical methods of PDEs especially the shock wave equation and high curvature turbulence equations. In chapter5we apply MQ quasi-difference for simulating boundary detection models. Compared with the level set method, our approach costs little time and be able to get the boundaries more precisely.Chapter6gives a simple method to simulate the famous Burgers-Fisher equation using one kind of MQ quasi-interpolation L_D Posteriori error estimate of this method is given.Chapter7presents a work summary and gives the plan of our future work.