| 摘要 | 第3-5页 |
| ABSTRACT | 第5-6页 |
| Chapter 1 Preface | 第9-12页 |
| Chapter 2 Numerical analysis of a pseudo-compact C-N conser-vative scheme for the Rosenau-KdV equation coupling with the Rosenau-RLW equation | 第12-34页 |
| 2.1 Introduction | 第12-14页 |
| 2.2 A pseudo-compact C-N conservative scheme and its discrete con-servative invariant | 第14-18页 |
| 2.3 Estimates and existence of difference solution | 第18-22页 |
| 2.4 Convergence and stability of the scheme | 第22-26页 |
| 2.5 Numerical experiments | 第26-34页 |
| Chapter 3 A high-accuracy conservative scheme for generalized regularized long-wave equation | 第34-50页 |
| 3.1 Introduction | 第34-35页 |
| 3.2 High-accuracy scheme and its discrete conservative law | 第35-38页 |
| 3.3 Solvability and estimate | 第38-40页 |
| 3.4 Convergence | 第40-44页 |
| 3.5 Numerical experiments | 第44-50页 |
| Chapter 4 On the convergence of a high-accuracy compact conser-vative scheme for the modified regularized long-wave equation | 第50-69页 |
| 4.1 Introduction | 第50-51页 |
| 4.2 The high-accuracy compact conservative vector difference scheme | 第51-54页 |
| 4.3 Discrete conservative property, estimate and solvability | 第54-59页 |
| 4.4 Convergence and stability of the difference solution | 第59-63页 |
| 4.5 Numerical experiments | 第63-68页 |
| 4.6 Conclusion | 第68-69页 |
| Chapter 5 On the convergence of a high-accuracy conservative scheme for the Zakharov equations | 第69-89页 |
| 5.1 Introduction | 第69-71页 |
| 5.2 High-accuracy compact conservative scheme | 第71-73页 |
| 5.3 Conservative properties and error estimates | 第73-77页 |
| 5.4 Convergence | 第77-82页 |
| 5.5 Numerical experiments | 第82-87页 |
| 5.6 Conclusion | 第87-89页 |
| Chapter 6 Conclusion and future work | 第89-91页 |
| 6.1 Conclusion | 第89页 |
| 6.2 Future work | 第89-91页 |
| Reference | 第91-99页 |
| Appdenix PAPERS PUBLISHED DURING PH.D | 第99-100页 |
| Appdenix THANKS | 第100页 |
