| 非线性分数阶微分方程的hp型Legendre谱配置法 |
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| 引用本文： | 李珊,安筱,孙桂磊.非线性分数阶微分方程的hp型Legendre谱配置法[J].上海理工大学学报,2022,44(4):368-372. |
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| 作者姓名： | 李珊 安筱 孙桂磊 |
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| 作者单位： | 上海理工大学 理学院，上海 200093 |
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| 基金项目： | 国家自然科学基金资助项目（12071294） |
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| 摘 要： | 研究了求解非线性分数阶微分方程的hp 型Legendre 谱配置法。首先提出将多分数阶微分方程转化成等价的Volterra 积分方程, 其次构造了近似求解原方程的数值方法, 最后通过数值实验说明了该算法的理论正确性以及所构造数值方法的有效性。
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| 关 键 词： | 非线性分数阶微分方程 Legendre谱配置法 hp型误差界 |
| 收稿时间： | 2021/6/29 0:00:00 |
An hp-version Legendre spectral collocation method for nonlinear fractional differential equations |
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| LI Shan,AN Xiao,SUN Guilei.An hp-version Legendre spectral collocation method for nonlinear fractional differential equations[J].Journal of University of Shanghai For Science and Technology,2022,44(4):368-372. |
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| Authors: | LI Shan AN Xiao SUN Guilei |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | The hp-version Legendre spectral collocation method for solving nonlinear fractional differential equations was studied. At first, the multifractional differential equation was transformed into an equivalent Volterra integral equation. Then a numerical method to approximate the original equation was constructed. Finally, the correctness of the algorithm theory and the effectiveness of the proposed numerical method were demonstrated by numerical experiments. |
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| Keywords: | nonlinear fractional differential equations Legendre spectral collocation method hp-version error bounds |
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