| Abstract in Chinese | 第1-5页 |
| Abstract in English | 第5-6页 |
| Preface | 第6-9页 |
| 1 Preliminaries | 第9-11页 |
| ·Compact dfifference scheme for the second derivative | 第9-10页 |
| ·Richardson extrapolation | 第10-11页 |
| 2 High-order algorithm for solving two-dimensional problem | 第11-27页 |
| ·Introduction | 第11页 |
| ·Fourth-order algorithm based on approximate factorization | 第11-15页 |
| ·Stability of the algorithm | 第15-17页 |
| ·Numerical approximation for nonlinear evolution equation | 第17-20页 |
| ·High-order accuracy in the temporal dimension | 第20-21页 |
| ·Numerical results | 第21-27页 |
| 3 High-order algorithm for solving three-dimensional problem | 第27-44页 |
| ·Introduction | 第27页 |
| ·Fourth-order algorithm based on approximate factorization | 第27-32页 |
| ·Stability of the algorithm | 第32-34页 |
| ·Numerical algorithm for solving nonlinear evolution equation | 第34-38页 |
| ·High-order accuracy in the temporal dimension | 第38页 |
| ·Numerical results | 第38-44页 |
| 4 Concluding remarks | 第44-45页 |
| Bibliography | 第45-47页 |
| Acknowledgements | 第47页 |
