Adomian多项式的计算及其在整数阶和分数阶非线性微分方程中的应用  

Calculation of Adomian polynomials and its applications to integer-order and fractional order nonlinear differential equations

作　　者：段俊生[1] 

机构地区：[1]上海应用技术学院理学院,上海201418

出　　处：《应用数学与计算数学学报》2015年第2期187-210,共24页Communication on Applied Mathematics and Computation

基　　金：上海市自然科学基金资助项目(14ZR1440800);上海市教育委员会科研创新基金资助项目(14ZZ161)

摘　　要：讨论分数阶微分方程和Adomian分解方法的应用.首先,回顾Adomian多项式的几种新的快速算法,包括单变量和多变量Adomian多项式.然后,讨论Rach-Adomian-Meyers修正分解方法、多级分解法和收敛加速概念,包括对角Pade近似和迭代Shanks变换.最后,研究Adomian分解法、修正分解法和收敛加速技术在分数阶微分方程求解中的应用.方法给出了容易计算、容易验证和迅速收敛的解析近似解序列.In this article, we discuss fractional order differential equations and the applications of the Adomian decomposition method. First, we review several new, fast algorithms for the Adomian polynomials, including the single variable and multivariable cases. Then, we discuss the Rach-Adomian-Meyers modified decomposition method, the multistage decomposition method, and the conver- gence acceleration concept, including the diagonal Pad~ approximants and the iterated Shanks transform. Finally, we investigate the applications of the Adomian decomposition method, the modified decomposition method, and the convergence acceleration techniques to the fractional order differential equations. The method gives an easily computable, readily verifiable and rapidly convergent sequence of analytic approximate solutions.

关 键 词：分数阶微积分 ADOMIAN分解方法 ADOMIAN多项式 非线性微分方程 

分 类 号：O174.14[理学—数学] O175.29[理学—基础数学]