A compact finite difference method for solving Burgers' equation |
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| Authors: | Shusen Xie Guangxing Li Sucheol Yi Sunyeong Heo |
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| Affiliation: | 1. School of Mathematical Sciences, Ocean University of China, Qingdao 266071, People's Republic of China;2. Department of Applied Mathematics, Changwon National University, Changwon 641‐773, Republic of Korea;3. Department of Statistics, Changwon National University, Changwon 641‐773, Republic of Korea |
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| Abstract: | In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd. |
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| Keywords: | Burgers' equation Hopf– Cole transformation compact difference scheme convergence stability |
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