Three Burgers Was Not Mq Radial Basis Function And Equation

The present dissertation are concerned with univariate quasi interpo-lation operators. This dissertation consists of five chapters:chapter I is devoted to the background of these problems, study of the current situation at home and abroad and innovation of this article.In chapter II, we introduce the theory of the radial basis function and summarize in detail the knowledge of the known quasi-interpolation.Chapter III roots in our research. In this chapter,we construct a quasi-interpolation operator to scattered data by the shifts of cubic multiquadric function, which does not require the derivatives at endpoints, so it is very practical, meantime, we have also proven that the operator possesses not only cubic polynomial reproduction property, but also shape preserving of order three and four and provide error estimate1/6∫a/bk30(x,t)f(4)(t)dt.At last in this chapter, we demonstrate some numerical examples, and compare to accuracy with operator Lp and LdIn chapter IV, we discuss the application of the quasi-interpolation with radial basis functions for numerical solving the partial differential equations. According to chapter three, we propose a new quasi interplati-on method to solve Burgers’equation. The underlying idea of our means is that:employing the first derivative of the quasi-interpolation to approx-imate the first spatial derivative and approximate the second spatial derivative use a first order difference on first spatial derivatives, while the approach of the time derivative is used a finite difference.In chapter V,we give a summary and outlook. We briefly review the main contents of this thesis, and propose some suggestions to the future work.