| 摘要 | 第1-8页 |
| Abstract | 第8-11页 |
| 1 Introduction | 第11-13页 |
| 2 Mixed Fourier-generalized Jacobi rational spectral method for two-dimensional exterior problems | 第13-32页 |
| ·Generalized Jacobi rational orthogonal approximations | 第13-17页 |
| ·Fourier orthogonal approximation | 第17页 |
| ·Mixed Fourier-generalized Jacobi rational orthogonal approximations | 第17-20页 |
| ·Spectral methods for exterior problems. | 第20-26页 |
| ·Linear Problem | 第20-21页 |
| ·Nonlinear problem | 第21-26页 |
| ·Numerical results | 第26-32页 |
| ·Linear problem | 第26-29页 |
| ·Nonlinear problem | 第29-32页 |
| 3 Generalized Jacobi rational spectral methods with essential imposition of Neumann boundary conditions | 第32-48页 |
| ·Notations and preliminaries | 第32-39页 |
| ·One-dimensional generalized Jacobi rational approximation | 第33-36页 |
| ·Two-dimensional generalized Jacobi rational approximation | 第36-37页 |
| ·Mixed Fourier-generalized Jacobi rational approximation | 第37-39页 |
| ·Spectral methods for problems with Neumann boundary conditions | 第39-42页 |
| ·Generalized Jacobi rational spectral method for one-dimensional problem | 第39-40页 |
| ·Generalized Jacobi rational spectral method for two-dimensional problem | 第40-41页 |
| ·Mixed Fourier-generalized Jacobi rational spectral method for exterior problem | 第41-42页 |
| ·Numerical results | 第42-48页 |
| References | 第48-51页 |
| 致谢 | 第51页 |
