摘要
Adomian分解方法是解微分方程的一种分析方法.基于Adomian分解方法和修正的渐近Adomian分解方法,给出了多步修正的渐近Adomian分解方法.指出修正的渐近Adomian分解方法可以给出非线性微分方程的精确解.多步修正的渐近Adomian分解方法也可以给出精确解且最小化计算量.一些数值例子表明多步修正的渐近Adomian分解方法的有效性.对于一些问题,多步修正的渐近Adomian分解方法是优于Adomian分解方法和修正的渐近Adomian分解方法.
The adomian decomposition method （ADM） is an analytical method for solving differential equations. Based on the ADM and modified asymptotic ADM, we give a multi-step modified asymptotic ADM. Moreover, we point out that the modified asymptotic ADM can give the exact solution to nonlinear dif- ferential equations. The multi-step modified asymptotic ADM has the minimal computational workload and provides the exact solution. Some examples are pre- sented to verify the validity of the multi-step modified asymptotic ADM. For these problems, the multi-step modified asymptotic ADM are superior to the ADM and the modified asymptotic ADM.
出处
《应用数学与计算数学学报》
2017年第2期224-240,共17页
Communication on Applied Mathematics and Computation
基金
supported by the National Natural Science Foundation of China(11372326,11432015,11501038)
the Beijing Outstanding Talents Foundation(2014000020124G108)
