| 一类变系数分数阶微分方程的数值解法 |
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| 引用本文： | 李宝凤.一类变系数分数阶微分方程的数值解法[J].数学杂志,2015,35(6):1353-1362. |
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| 作者姓名： | 李宝凤 |
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| 作者单位： | 唐山师范学院数学与信息科学系, 河北 唐山 063000 |
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| 基金项目： | Supported by the Natural Foundation of Hebei Province(A2012203047) and Natural Science foundation of Tangshan Normal University(2014D09). |
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| 摘 要： | 本文研究了一类变系数分数阶微分方程的数值解法问题. 利用Cheyshev小波推导出的分数阶微分方程的算子矩阵把分数阶微分方程转换为代数方程组. 同时给出了Cheyshev小波基的收敛性和误差估计表达式, 并给出数值算例说明所提方法的精确性和有效性
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| 关 键 词： | 分数阶积分 Chebvshev小波 算子矩阵 分数阶微分方程 block pulse函数 |
| 收稿时间： | 2013/5/3 0:00:00 |
| 修稿时间： | 2014/5/30 0:00:00 |
A NUMERICAL METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS |
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| LI Bao-feng.A NUMERICAL METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS[J].Journal of Mathematics,2015,35(6):1353-1362. |
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| Authors: | LI Bao-feng |
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| Institution: | Dep. of Math and Info. Sci., Tangshan Normal University, Tangshan 063000, China |
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| Abstract: | Here is to study the numerical solution of multi-order fractional differential equa-tions (FDEs) with variable coefficients. We derive the operational matrix of fractional integration based on the Chebyshev wavelets. The operational matrix of fractional integration is utilized to reduce the fractional differential equations to a system of algebraic equations. In addition, the convergence of the Chebyshev wavelet bases and the error estimation expression are presented. A numerical example is provided to demonstrate the accuracy and efficiency of the proposed method. |
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| Keywords: | fractional integration the Chebyshev wavelets operational matrix fractional differential equations block pulse function |
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