Summary: We consider the following neutral functional-differential equations with proportional delays
with the initial conditions
The reproducing kernel Hilbert space method (RKHSM) is applied to (1), (2). Its approximate solution is obtained by truncating the -term of exact solution. Some examples are displayed to demonstrate the computation efficiency of the method. We also compare the performance of the method with a particular Runge-Kutta method, a one-leg -method and variational iteration method. Experimental results indicate that the RKHSM is an accurate and efficient method for the solution of neutral functional-differential equations with proportional delays.