A New Wavelet Collocation Algorithm for Solving a Nonlinear Boundary Value Problem of the Human Corneal Shape.

Abstract

The Hermite wavelet method (HWM) is introduced in this study to solve a nonlinear differential equation determining the human corneal morphology. The changes in curvature of the human cornea in hypotony, normal intraocular pressure, glaucoma, and other conditions are discussed. The Hermite wavelet operational matrices of derivatives are used to generate wavelet solutions based on this technique. The solutions of the nonlinear differential equation are determined for various values of constant parameters that can appear in the diverse physical situations. The proposed wavelet solutions are more accurate than the other approximate analytical solutions listed in the literature. The HWM solutions are compared to homotopy perturbation method, Taylor series, pertur-bation technique and artificial neural network solutions. There is broad consensus. This illustrates that HWM is a useful and appropriate strategy for handling difficulties with nonlinear boundary value problems that emerge in corneal geometry.