线性分段连续型延迟微分方程的变分迭代解法

Variational Iteration Method for Linear Differential Equation with Piecewise Continuous Arguments

主要利用变分迭代法求解自变量分段连续型延迟微分方程的初值问题,由变分理论得到了拉格朗日乘子,进而构造了迭代关系式,在不同的区间上求得了各阶解析近似解,并且证明了收敛性,连续级数收敛结果和真实解的形式一致.通过具体的实例验证了该方法的有效性和可靠性.

This paper deals with the problem of delay differential equation with piecewise continuous arguments.The lagrange multiplier is obtained according to the theory ofvariation,then the iteration formula is constructed. Moreover,the analytical approximation solutions in different intervals are given and the convergence is proved. Finally,the theoretical results are verified by some some numerical examples.