Padé Approximation And Its Applications

Padéapproximation is a special type of rational approximations,which has many applications in various computation problems of science and technology.This thesis reviews some essential properties of Padéapproximation and puts focus on its applications on the filter designs and numerical methods to partial differential equations.The thesis is organized as follows.Chapter 1 introduces the classical definition of Padéapproximation and its explicit expressions.Chapter 2 discusses some research results of the convergence of rows of the Padéapproximants,and emphasizes the convergence of rows of the Padéapproximation to the functions that have several poles of maximal multiplicity or that have several branching points.Chapter 4 reviews some applications of Padéapproximations,especially the numerical methods that consolidate the ADM and Padéapproximation to solve some nonlinear partial differential equations.Especially gives a new solution of fKdV equation.The last chapter summarizes the thesis and proposes some open questions.The new results are in Chapter 3,where it shows how to make use of the convergence of rows of the Padéapproximation to simulate the lower-order poles of transform functions so as to design digital filters,and in Chapter 4,where it offers a new algorithm of Padé-ADM method to solve fKdV equation.