Generalized Jacobi Function Spectrum And Pseudospectral Methods For Burgers Equation On Full Lines

In this thesis,we study the spectral and pseudospectral methods of Burgers equation on the whole line by using generalized Jacobi functions.Firstly,we introduce the definitions and properties of classical Jacobi polynomials and generalized Jacobi functions,and derive the orthogonal projection and interpolation approximation errors of the needed generalized Jacobi functions.Then,we choose the appropriate mapping,transform the Burgers equation on the whole line into the equation in bounded domain,which simplifies the theoretical analysis and numerical calculation.We propose a spectral scheme of the transformed equation,prove the stability and convergence of the proposed scheme,and give a detailed numerical implementation.Numerical results demonstrate the efficiency of the proposed algorithm.Next,we propose a pseudospectral scheme of the transformed equation,analyze the stability and convergence of the scheme.Ample numerical results valid the high accuracy of the proposed new approach.