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| 一类分数阶常微分方程初值问题的预校算法 | |
| 引用本文： | 陈全发,冯光,傅尧.一类分数阶常微分方程初值问题的预校算法[J].计算数学,2009,31(4). |
| 作者姓名： | 陈全发 冯光 傅尧 |
| 作者单位： | 1. 湘南学院数学系,湖南郴州,423000 2. 湘潭大学数学与计算科学学院,湖南湘潭,411105 3. 江西渝州科技职业学院数学系,江西新余,338000 |
| 基金项目： | 湖南省自然科学基金联合基金，湖南省教育厅科研项目 |
| 摘 要： | 利用Caputo导数的性质和二次多项式插值逼近,导出了分数阶二次多项式插值逼近隐式算法的完整计算公式,证明了其整体误差估计为O(hβ),β=min{2+α,3};在此基础上,构造了一类求解分数阶常微分方程初值问题的新的预校算法, 证明了其整体误差估计为 O(hγ),γ=min{2α,2+α,3},并通过数值实例得以验证. |
| 关 键 词： | 分数阶微分方程 Caputo导数 插值逼近 预校算法 误差分析 |
PREDICTOR-CORRECTOR METHOD FOR A CLASS OF INITIAL VALUE PROBLEMS OF FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS |
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| Chen Quanfa,Feng Guang,Fu Yao.PREDICTOR-CORRECTOR METHOD FOR A CLASS OF INITIAL VALUE PROBLEMS OF FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS[J].Mathematica Numerica Sinica,2009,31(4). | |
| Authors: | Chen Quanfa Feng Guang Fu Yao |
| Abstract: | According to the properties of the Caputo derivative and a second-degree polynomial interpolation approximation, an implicit numerical scheme on interpolation approximation is derived completely, and its global error is estimated to be O(h~β),β = min{2 + α, 3}. Moreover, a predictor-corrector method for a class of initial value problems of fractional ordinary differential equations with higher convergence order was presented, and its global error is estimated to be O(h~γ), γ = min{2 + α, 2α, 3}, and numerical examples verify the efficiency of the numerical method. |
| Keywords: | Fractional differential equation Caputo derivatives Interpolation approximation Predictor-corrector method Error analysis |
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