Next Article in Journal
Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation
Previous Article in Journal
Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle

An Efficient Semi-Analytical Solution of a One-Dimensional Curvature Equation that Describes the Human Corneal Shape

Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, UAE
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 8; https://doi.org/10.3390/mca24010008
Received: 8 December 2018 / Revised: 5 January 2019 / Accepted: 8 January 2019 / Published: 10 January 2019
  |  
PDF [382 KB, uploaded 17 January 2019]
  |  

Abstract

In this paper, a numerical approach is proposed to find a semi analytical solution for a prescribed anisotropic mean curvature equation modeling the human corneal shape. The method is based on an integral operator that is constructed in terms of Green’s function coupled with the implementation of Picard’s or Mann’s fixed point iteration schemes. Using the contraction principle, it will be shown that the method is convergent for both fixed point iteration schemes. Numerical examples will be presented to demonstrate the applicability, efficiency, and high accuracy of the proposed method. View Full-Text
Keywords: semi-analytical solution; curvature equation; fixed point iteration; Green’s function semi-analytical solution; curvature equation; fixed point iteration; Green’s function
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Abukhaled, M.; Khuri, S. An Efficient Semi-Analytical Solution of a One-Dimensional Curvature Equation that Describes the Human Corneal Shape. Math. Comput. Appl. 2019, 24, 8.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top