| Caputo分数阶反应-扩散方程的隐式差分逼近 |
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| 引用本文： | 陈景华.Caputo分数阶反应-扩散方程的隐式差分逼近[J].厦门大学学报(自然科学版),2007,46(5):616-619. |
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| 作者姓名： | 陈景华 |
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| 作者单位： | 厦门大学数学科学学院,福建,厦门,361005 |
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| 摘 要： | 分数阶微分方程在许多应用科学上比整数阶微分方程更能准确地模拟自然现象.本文考虑分数阶反应-扩散方程.将一阶的时间偏导数用Caputo分数阶导数替换,并给出了一个隐式的差分格式.利用能量方法给出此差分格式的稳定性与收敛性证明,最后用数值例子说明差分格式是有效的.
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| 关 键 词： | 分数阶反应-扩散方程 Caputo导数 能量方法 稳定性 收敛性 |
| 文章编号： | 0438-0479（2007）05-0616-04 |
| 修稿时间： | 2006-10-27 |
An Implicit Approximation for the Caputo Fractional Reaction-Dispersion Equation |
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| CHEN Jing-hua.An Implicit Approximation for the Caputo Fractional Reaction-Dispersion Equation[J].Journal of Xiamen University(Natural Science),2007,46(5):616-619. |
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| Authors: | CHEN Jing-hua |
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| Institution: | School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
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| Abstract: | Fractional differential equations can more correctly simulate many phenomena contrasting with integer differential equations in lost of applied science.In this paper,a time-fractional reaction-dispersion equation was considered which the first order derivative was replaced by a Caputo fractional derivative,and an implicit difference scheme was given.Stability and convergence were proved by using energy method.A numerical example demonstrates the difference method is effective. |
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| Keywords: | fractional reaction-dispersion equation Caputo fractional derivative difference scheme stability convergence |
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