吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
Journal of Jilin University (Science Edition)
2015年
5期
851-856
,共6页
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
Adomian 分解法%Adomian 多項式%分數階積分方程組%收斂性分析%截斷誤差
Adomian 분해법%Adomian 다항식%분수계적분방정조%수렴성분석%절단오차
Adomian decomposition method%Adomian polynomials%systems of integral equations of fractional order%convergence analysis%truncated error
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。
通過 Adomian 分解法求解非線性分數階 Volterra 積分方程組的數值解。將多元Adomian多項式與分數階積分定義有效結閤，得到瞭 Adomian 級數解；結閤 Laplace 變換討論級數解的收斂性，證明瞭所得級數解收斂于精確解，併給齣最大絕對截斷誤差。數值算例錶明，該方法可行、有效。
통과 Adomian 분해법구해비선성분수계 Volterra 적분방정조적수치해。장다원Adomian다항식여분수계적분정의유효결합，득도료 Adomian 급수해；결합 Laplace 변환토론급수해적수렴성，증명료소득급수해수렴우정학해，병급출최대절대절단오차。수치산례표명，해방법가행、유효。
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.
