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研究生:謝薰仰
研究生(外文):Hsun-Yang, Hsieh
論文名稱(外文):Conservative Finite Difference Schemes For Regularized Long-wave Equation
指導教授:卓建宏卓建宏引用關係
指導教授(外文):Chien-Hong, Cho
口試委員:黃子偉曾睿彬
口試委員(外文):Zih-Wei, HwangJui-Pin, Tseng
口試日期:2012-07-10
學位類別:碩士
校院名稱:國立中正大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:18
中文關鍵詞:有限差分法正則長波方程穩定性
外文關鍵詞:finite difference schemeRLW equationconvergencestability
相關次數:
  • 被引用被引用:0
  • 點閱點閱:172
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  • 下載下載:13
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In this paper, a finite difference method for the regularized long-wave equation is considered. We propose an energy-conserved finite difference scheme. It is proved that the finite difference scheme is stable and converges in the order O(h+\tau). We also report several numerical results which show that our method is reliable.
1 Introduction 3
2 Preliminaries 4
2.1 Zhang’s scheme for (5) [10] 4
2.2 Koide’s and Furihata’s schemes for (1) [5]5
3 Conservative schemes 8
4 Convergence and stability 9
5 Numerical simulations 12
6 Conclusion 12
Reference 13
[1] T. Achouri, N. Khiari and K. Omrani, On the convergence of difference schemes for the Benjamin-Bona-Mahony (BBM) equation, Appl. Math. Comput. 182 (2006) 999–1005.
[2] T.B. Benjamin, J.L. Bna and J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. R. Soc. London Ser. A. 272 47–78 (1972).
[3] J.C. Eilbeck and G.R. McGuire, Numerical study of the regularized long-wave equation, I: Numerical methods, J. Comput. Phys. 19 43–57 (1975).
[4] J.C. Eilbeck and G.R. McGuire, Numerical study of the regularized long-wave equation, II: Numerical methods, J. Comput. Phys. 23 63–73 (1977).
[5] S. Koide, D. Furihata, Nonlinear and Linear Conservative Finite Difference Schemes for Regularized Long Wave Equaion, Japan J. Indust. Appl. Math. 26 15–40 (2009).
[6] K. Omrani, F. Abidi, T. Achouri, N. Khiari, A new conservative finite difference scheme for the Rosenau equation, Appl. Math. Comput. 201 35–43 (2008).
[7] P.J. Olver, Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc. 85 143–160 (1979).
[8] P. Rosenau, Dynamics of the dense discrete systems, Prog. Theor. Phys. 79 (1988) 1028–1042.
[9] DU Yu, XU You-Cai, HU Bing, Three Level Finite Difference Scheme For Rosenau-Burgers Equation, Journal of Sichuan University (Natural Science Edition) 47 1–6 (2010).
[10] L. Zhang, A finite difference scheme for generalized regularized long-wave equation, Appl. Math. Comput. 168 962–972 (2005).
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