Jacobi谱方法及其对奇异问题、无界区域问题和轴对称区域问题的应用PDF电子书下载

Chapter 1 Introduction 1

1.1 Motivation of the research 1

1.2 An Outline of the Dissertation 6

Chapter 2 Preliminaries 9

2.1 Notations and function spaces 9

2.2 Jacobi polynomials 11

Chapter 3 Jacobi Interpolation Approximations to One Dimensional problems 15

3.1 Some inverse inequalities and imbedding inequalities 16

3.2 Jacobi polynomial approximations in one dimension 25

3.3 Jacobi interpolation approximation in one dimension 50

3.4 Some applications 65

3.5 Numerical results 84

Chapter 4 Jacobi Spectral Methods ForMultiple Dimensional Problems 90

4.1 Non-isotropic Jacobi approximations in multiple dimensions 91

4.2 Some applications 124

4.3 Numerical algorithms 141

4.4 Numerical results 150

Chapter 5 Jacobi Pseudospectral Method For Multiple Dimensional Problems 156

5.1 Jacobi interpolation approximations in multiple dimensions 157

5.2 Some applications 172

Appendix 184

References 188

Acknowledgement 194