非线性方程算子分解算法的收敛性

Convergence of the decomposition method for solving nonlinear equations

算子分解算法是求解各种类型的非线性方程的一种新的、有效的方法，其有效性依赖于方程及解的性质．在对Ａｄｏｍｉａｎ多项式Ａｎ的结构进行分析的基础上，证明了函数项级数的一致收敛性，从而保证了算子分解算法的收敛性和有效性．

The decomposition method provides a new, efficient computational procedure for solving large classes of nonlinear equations. The procedure depends on the calculation of the Adomians plynomials A n. Another definition of A n is given in this paper. Based on this definition, the convergence of the series ∑∞n=0 A n in a Banach space X is proved, which ensures the convergence of the method.