Analytic solutions to a class of nonlinear infinite-delay-differential equations

The infinite-delay-differential equations (IDDEs) are studied and the analytic solution of a class of nonlinear IDDEs is presented based on the characteristics of the reproducing kernel space W2[0,∞). Besides, the exact solution is represented in the form of series. It is proved that the n-term approximation un(x) converges to the exact solution u(x) of the IDDEs. Moreover, the approximate error of un(x) is monotone decreasing. The results of experiments showed that the proposed method in this paper is computationally efficient.