Adomian分解法求解非线性分数阶Volterra积分方程组  

Adomian Decomposition Method for Sloving Systems of Nonlinear Volterra Integral Equations of Fractional Order

作　　者：全晓静[1] 韩惠丽[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《吉林大学学报（理学版）》2015年第5期851-856,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11261041;11261045)

摘　　要：通过Adomian分解法求解非线性分数阶Volterra积分方程组的数值解.将多元Adomian多项式与分数阶积分定义有效结合,得到了Adomian级数解;结合Laplace变换讨论级数解的收敛性,证明了所得级数解收敛于精确解,并给出最大绝对截断误差.数值算例表明,该方法可行、有效.During solving the numerical solution of systems of nonliner Volterra integral equations of fractional order by the Adomian decomposition method,the Adomian series solution was obtained by combining the multivariable Adomian polynomials with the definition of fractional order integral.At the same time,the convergence of the series solution was discussed with the help of Laplace transform.It was shown that the series solution converged to the exact solution.And the maximum absolute truncated error of the Adomian series solution was also given.Finally,effectiveness and feasibility of the proposed Adomian decomposition method were shown by numerical example.

关 键 词：ADOMIAN分解法 ADOMIAN多项式 分数阶积分方程组 收敛性分析 截断误差 

分 类 号：O175.6[理学—数学]