| 摘要 | 第1-5页 |
| Abstract | 第5-6页 |
| Contents | 第6-7页 |
| Chapter 1: Some background of Landau-Lifshitz equation | 第7-11页 |
| Chapter 2: Convergence and stability of the difference scheme | 第11-29页 |
| ·Introduction of the difference scheme | 第11-13页 |
| ·Existence of the solution and the stability of the scheme | 第13-21页 |
| ·Numerical Experiments and Conclusions | 第21-29页 |
| Chapter 3: Convergence of the Semi-dicrete Fourier Spectral Methods | 第29-41页 |
| ·Definition and Lemmas | 第29-31页 |
| ·Semi-discrete Fourier Spectral Method and Error Estimates | 第31-34页 |
| ·Numerical Experiments about the free plane case | 第34-41页 |
| Chapter 4: Exact periodic and blow up solutions for 2D Ginzburg-Landau equation | 第41-50页 |
| ·Introduction | 第41-42页 |
| ·The general form of solution | 第42-44页 |
| ·Periodic and blow up solutions | 第44-47页 |
| ·The subcases solution about (4.19) | 第44-46页 |
| ·Blow up solutions | 第46-47页 |
| ·Graphs for the solutions | 第47-50页 |
| Appendix A | 第50-54页 |
| Appendix B | 第54-58页 |
| References | 第58-60页 |
| The results achieved during the relevant degree | 第60-62页 |
| Acknowledgements | 第62-63页 |
