[1]全晓静,韩惠丽,王健.Adomian分解法求解非线性分数阶Volterra积分方程[J].江西师范大学学报(自然科学版),2014,(05):517-520.
　QUAN Xiao-jing,HAN Hui-li,WANG Jian.The Adomian Decomposition Method for Sloving Nonlinear Volterra Integral Equations of Fractional Order[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(05):517-520.
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Adomian分解法求解非线性分数阶Volterra积分方程()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年05期
页码:
517-520
栏目:
出版日期:
2014-10-31

文章信息/Info

Title:
The Adomian Decomposition Method for Sloving Nonlinear Volterra Integral Equations of Fractional Order
作者:
全晓静;韩惠丽;王健
宁夏大学数学计算机学院,宁夏 银川,750021
Author(s):
QUAN Xiao-jing；HAN Hui-li；WANG Jian
关键词:
分数阶积分方程; Adomian多项式; 收敛性分析; 误差估计
Keywords:
fractional integral equation; Adomian polynomials; convergence analysis; error estimate
分类号:
O175.5
文献标志码:
A
摘要:
Adomian 分解法求解非线性分数阶 Volterra 积分方程的数值解，将 Adomian 多项式与积分方程的定义相结合，得出一个递推公式求解方程的级数解，并进行了收敛性分析，给出了级数解的最大绝对截断误差，通过数值算例说明了该方法的有效性和可行性。
Abstract:
Application of Adomian decomposition method,series solution of nonlinear volterra integral equations of fractional order are approximately obtained. The equation is solved by combining Adomian polynomials with the defi-nition of fractional order integral. Convergence of the series solution is proved and the maximum absolute truncated error of the Adomian series solution is also given. Thus,the effectiveness and feasibility of the Adomian decomposi-tion method are illustrated by the numerical example.

参考文献/References:

[1] Lepik U.Sloving fractional integral equation by the Haar wavelet method [J].Applied Mathematics and Computation,2009,214(2):468-478.
[2] 朱双云,苗福生,韩惠丽.分数阶第一类Volterra积分方程小波数值解 [J].宁夏大学学报:自然科学版,2012,33(2):130-134.
[3] Adomian G.Stochastic system [M].New York:Academic Press,1983.
[4] Adomian G.A review of decomposition method in applied mathematics [J].Joural of Mathematics Analysis and Application,1988,135(2):501-544.
[5] 梁祖峰,唐晓艳.用Adomian 分解法求解分数阻尼梁的解析解 [J].应用数学和力学,2007,28(2):200-208.
[6] Duan Junsheng,Randolph Rach,Dumitru Baleanu,et al.A review of the Adomian decomposition method and its applications to fractional differential equations [J].Commun Frac Calc,2012,3(2):73-99.
[7] El-Kalla I L.Convergence of the Adomian method applied to a class of nonlinear integral equations [J].Applied Mathematics Letters,2008,21(4):372-376.
[8] Behiry S H,Abd-Elmonem R A,Gomaa A M.Discrete Adomian decomposition solution of nonlinear fredholm integral equation [J].Ain Shams Engineering Journal,2010,1(1):97-101.
[9] 单锐,魏金侠,张雁,等.Adomian分解法求解二维非线性Volterra积分方程的数值解 [J].黑龙江大学自然科学学报,2012,29(5):573-577.
[10] 黄洁,韩惠丽.应用Legendre小波求解非线性分数阶Volterra积分微分方程 [J].吉林大学学报:理学版,2014,52(4):655-660.
[11] 张倩,韩惠丽,张盼盼.基于有理Haar小波求解分数阶第2类Fredholm积分方程 [J].江西师范大学学报:自然科学版,2014,38(1):47-50.
[12] 陈一鸣,刘丽丽,孙璐,等.Adomain分解法求解非线性分数阶Fredholm积分微分方程 [J].应用数学,2013,26(4):785-790.
[13] 朱红玲,郝玲,余志先,等.Adomain分解法求解非线性分数阶积分微分方程 [J].辽宁工程技术大学学报:自然科学版,2013,32(1):132-135.
[14] 陈一鸣,孙慧,刘乐春,等.Legendre多项式求解变系数的分数阶Fredholm积分微分方程 [J].山东大学学报:理学版,2013,48(6):80-86.
[15] 仪明旭,陈一鸣,魏金侠,等.应用Haar小波求解非线性分数阶Fredholm积分微分方程 [J].河北师范大学学报:自然科学版,2012,36(5):452-455.

备注/Memo

备注/Memo:
国家自然科学基金(11261041)
更新日期/Last Update: 1900-01-01