解分数阶微分代数系统的Adomian分解方法  

On the Solution of Fractional Differential-Algebraic Systems With the Adomian Decomposition Method

作　　者：冯再勇[1,2] 陈宁[1] 

机构地区：[1]南京林业大学机械电子工程学院,南京210037 [2]南京铁道职业技术学院社科部,南京210031

出　　处：《应用数学和力学》2015年第11期1211-1218,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11272159)~~

摘　　要：研究了利用Adomian分解求解分数阶微分代数系统的方法.分析了代数约束对Adomian方法求解的影响,指出直接解出代数约束变量,将原系统转化为微分系统进行Adomian分解的困难.提出确定代数变量级数解各分量的新方法,据此进行Adomian分解,得到整个系统的级数解.特别研究了代数约束为线性的分数阶微分代数系统的Adomian解法,证明了各变量间的线性代数约束关系可以转化为相应级数解中各分量的线性关系,从而方便求解,并结合具体例子证明了该方法简便有效.The solution of the fractional differential-algebraic systems （FDASs） was studied with the Adomian decomposition method. The influence of the algebraic constraints on the Ado- mian decomposition method was investigated, and the main difficulty of transforming the FDASs into fractional differential systems through solving the algebraic constraints directly was pointed out. To determine the components of the algebraic variable series solution, a new meth- od was presented with the Adomian decomposition implemented successfully to obtain the solu-tion of the FDAS. The solution of the FDAS under linear algebraic constraints was particularly discussed with the Adomian decomposition method. It＇ s proved that the linear relationship between the variables under algebraic constraints could be equivalently transformed into the linear relationship between the components of the corresponding series solution. 2 examples were given to illustrate the convenience and effectiveness of the proposed method.

关 键 词：分数阶 微分代数系统 Adomian分解 级数解 线性约束 

分 类 号：O155[理学—数学]