Rajaraman R, Hariharan G
Saveetha Engineering College Tamil Nadu India.
SASTRA Deemed University, Tamil Nadu India.
Nonlinear Dynamics Psychol Life Sci. 2023 Oct;27(4):381-395.
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.
本研究引入了埃尔米特小波方法（HWM）来求解一个确定人眼角膜形态的非线性微分方程。讨论了低眼压、正常眼压、青光眼及其他情况下人眼角膜曲率的变化。基于该技术，利用导数的埃尔米特小波运算矩阵来生成小波解。针对各种可能出现在不同物理情形中的常参数值，确定了非线性微分方程的解。所提出的小波解比文献中列出的其他近似解析解更精确。将HWM解与同伦摄动法、泰勒级数、摄动技术和人工神经网络解进行了比较。存在广泛共识。这表明HWM是处理角膜几何学中出现的非线性边值问题困难的一种有用且合适的策略。
