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

Abstract 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 W 2 [ 0 , ∞ ) . Besides, the exact solution is represented in the form of series. It is proved that the n-term approximation u n ( x ) converges to the exact solution u ( x ) of the IDDEs. Moreover, the approximate error of u n ( x ) is monotone decreasing. The results of experiments showed that the proposed method in this paper is computationally efficient.

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