Approximate Analytical Solutions for a Nonlinear Model of Corneal Curvature Using the Homotopy Perturbation Method in Conjunction with the Least Squares Method

In this paper we apply the Homotopy Perturbation Method in conjunction with the Least Squares Method to obtain, in a simple and straightforward manner, analytical approximations of the solutions for the nonlinear models of the corneal curvature. The partially linearized version of the model is extensively studied, and we included a comparison with previous results obtained by other well-known methods. On the other hand, for the fully nonlinear version of the model, we introduce for the first time an accurate analytical approximation of the solution.