| KdV方程的一类本性并行差分格式 |
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| 引用本文： | 王文洽.KdV方程的一类本性并行差分格式[J].应用数学学报,2006,29(6):995-1003. |
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| 作者姓名： | 王文洽 |
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| 作者单位： | 山东大学数学与系统科学学院,济南,250100 |
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| 摘 要： | 对三阶KdV方程给出了—组非对称的差分公式,并用这些差分公式和对称的Crank-Nicolson型公式构造了一类具有本性并行的交替差分格式．证明了格式的线性绝对稳定性．对—个孤立波解、二个孤立波解和三个孤立波解的情况分别进行了数值试验,并对—个孤立波解的数值解的收敛阶和精确性进行了试验和比较．
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| 关 键 词： | Korteweg-de Vries方程 本性并行 交替分段Crank-Nicolson差分格式 线性绝对稳定 |
| 收稿时间： | 2004-09-10 |
| 修稿时间： | 2004-09-102005-05-30 |
Difference Schemes with Intrinsic Parallelism for the KdV Equation |
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| WANG WENQIA.Difference Schemes with Intrinsic Parallelism for the KdV Equation[J].Acta Mathematicae Applicatae Sinica,2006,29(6):995-1003. |
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| Authors: | WANG WENQIA |
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| Institution: | School of Mathematics and System Sciences, Shandong University, Jinan 250100 |
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| Abstract: | A group of asymmetric difference schemes to approach the Korteweg-de Vries (KdV) equation is given here. Using the schemes and the symmetric Crank-Nicolson type scheme, the alternating difference scheme for solving the KdV equation is constructed. The scheme is unconditionally stable by analysis of linearization procedure. The results of the numerical experiments for the cases of single soliton solution and double solition and triple soliton are given. |
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| Keywords: | KdV equation intrinsic pallelism alternating segment Crank-Nicolson difference scheme unconditionally linear stable |
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