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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
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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
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
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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.

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