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| 用分数阶高阶近似法解非线性分数阶常微分方程组 | |
| 引用本文： | 林永华,庄平辉,刘发旺.用分数阶高阶近似法解非线性分数阶常微分方程组[J].厦门大学学报(自然科学版),2007,46(6):765-769. |
| 作者姓名： | 林永华 庄平辉 刘发旺 |
| 作者单位： | 1. 莆田学院 2. 厦门大学数学科学学院,福建,厦门,361005 3. 昆士兰理工大学数学科学学院,布利斯本,昆士兰,4001,澳大利亚 |
| 基金项目： | 莆田学院校科研和教改项目 |
| 摘 要： | 考虑非线性分数阶常微分方程组,利用Riemann-Liouville分数阶导数的高阶近似,建立分数阶微分方程组的高阶差分格式,并证明了该方法的相容性、收敛性和稳定性.最后给出数值例子,证实了分数阶高阶近似法是解非线性分数阶常微分方程组的有效方法. |
| 关 键 词： | 分数阶高阶近似法 非线性分数阶常微分方程组 相容性 收敛性 稳定性 |
| 文章编号： | 0438-0479（2007）06-0765-05 |
| 修稿时间： | 2007-05-09 |
Solving a System of Nonlinear Fractional Ordinary Differential Equations by Using Fractional High Order Approximation Methods |
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| LIN Yong-hua,ZHUANG Ping-hui,LIU Fa-wang.Solving a System of Nonlinear Fractional Ordinary Differential Equations by Using Fractional High Order Approximation Methods[J].Journal of Xiamen University(Natural Science),2007,46(6):765-769. | |
| Authors: | LIN Yong-hua ZHUANG Ping-hui LIU Fa-wang |
| Institution: | 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China; 2. School of Mathematical Sciences,Queensland University of Technology, GPO Box 2434,Brisbane, Qld. 4001, Australia |
| Abstract: | In this paper,a system of the nonlinear fractional ordinary differential equations is considered.In light of the high order approximation for the Rieman-Liouville fractional-order derivative,the difference scheme of the nonlinear fractional ordinary differential equations is constructed.The consistence,convergence and stability of the methods are also proved.Then a numerical example is provided to show that the methods are effective in solving a system of the nonlinear fractional ordinary differential equations. |
| Keywords: | fractional high order approximation methods nonlinear fractional ordinary differential equations system consistence convergence stability |
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