| 空间分数阶Edwards-Wilkinson方程的显式差分近似 |
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| 引用本文： | 马亮亮,田富鹏.空间分数阶Edwards-Wilkinson方程的显式差分近似[J].沈阳大学学报,2013,25(3):250-252. |
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| 作者姓名： | 马亮亮 田富鹏 |
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| 作者单位： | 1. 攀枝花学院数学与计算机学院,四川攀枝花,617000
2. 西北民族大学现代技术教育学院,甘肃兰州,730030 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 考虑一种空间分数阶Edwards-Wilkinson方程,这个方程是将一般的空间二阶导数用α(1<α≤2)阶导数代替.利用G算法对空间二阶导数进行离散,构建了空间分数阶Edwards-Wilkinson方程的显式有限差分格式,并证明了此差分格式是无条件稳定和收敛的,且具有o(τ)+o(h)收敛阶.
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| 关 键 词： | 空间分数阶 Edwards-Wilkinson方程 差分格式 稳定性 收敛性 |
An Explicit Difference Approximation for Space Fractional Edwards-Wilkinson Equation |
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| Ma Liangliang
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Tian Fupeng.An Explicit Difference Approximation for Space Fractional Edwards-Wilkinson Equation[J].Journal of Shenyang University,2013,25(3):250-252. |
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| Authors: | Ma Liangliang Tian Fupeng |
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| Institution: | 1. College of Mathematics and Computer, Panzhihua University, Panzhihua 617000, China; 2. College of Modern Education, Northwest University for Nationalities, Lanzhou 730030, China) |
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| Abstract: | A space fractional Edwards-Wilkinson equation is considered. The equation is obtained from the classical Edwards-Wilkinson equation by replacing the second-order space derivative with fractional derivative of order a（1〈a≤2）. Then an explicit difference scheme is presented by using the algorithm of G for the second-order space derivative. It is shown that the scheme is unconditional stable and convergence respectively, the convergence order of the scheme is o（r）＋o（h）. |
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| Keywords: | space-fractional derivative Edwards-Wilkinson equation difference scheme stability convergence |
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