Numerical solution of neutral functional-differential equations with proportional delays

In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs) with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.