A nonlinear mathematical model of the corneal shape

被引：31
作者：
Okrasinski, Wojciech [1 ]
Plociniczak, Lukasz [1 ]
机构：
[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50372 Wroclaw, Poland
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2012年 / 13卷 / 03期
关键词：
Corneal shape; Mathematical model; Nonlinear differential equation; Boundary value problem;
D O I：
10.1016/j.nonrwa.2011.11.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a nonlinear two-point boundary value problem which is derived as a description of corneal shape. We prove some basic results concerning existence, uniqueness and estimates. We suggest some approximate solution fitting over fifteen thousands real corneal data points with an error of order of 1%. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1498 / 1505
页数：8
相关论文
共 50 条
  • [41] Influence of corneal shape parameters on corneal deformation responses measured with a Scheimpflug camera
    Jing Liu
    Yan Wang
    Haohan Zou
    Mengdi Li
    International Ophthalmology, 2021, 41 : 2853 - 2859
  • [42] On a Nonisothermal Consolidation Mathematical Model of Geoinformatics
    Bulavatsky, V. M.
    Skopetsky, V. V.
    JOURNAL OF AUTOMATION AND INFORMATION SCIENCES, 2010, 42 (12) : 1 - 12
  • [43] A novel nonlinear SAZIQHR epidemic transmission model: mathematical modeling, simulation, and optimal control
    Kumar, Abhishek
    Tanvi, Rajiv
    Aggarwal, Rajiv
    PHYSICA SCRIPTA, 2025, 100 (01)
  • [44] Mathematical model and nonlinear finite element equation for reservoir fluid-solid coupling
    Zhang Guang-ming
    Liu He
    Zhang Jin
    Wu Heng-an
    Wang Xiu-xi
    ROCK AND SOIL MECHANICS, 2010, 31 (05) : 1657 - 1662
  • [45] SOLUTION OF THE MATHEMATICAL MODEL OF A NONLINEAR DIRECT CURRENT CIRCUIT USING PARTICLE SWARM OPTIMIZATION
    Amaya, Ivan
    Cruz, Jorge
    Correa, Rodrigo
    DYNA-COLOMBIA, 2012, 79 (172): : 77 - 84
  • [46] TOPOGRAPHIC ANALYSIS OF THE CHANGES IN CORNEAL SHAPE DUE TO AGING
    HAYASHI, K
    HAYASHI, H
    HAYASHI, F
    CORNEA, 1995, 14 (05) : 527 - 532
  • [47] Ocular Aberrations and Corneal Shape in Adults with and without Astigmatism
    Leung, Tsz-wing
    Lam, Andrew Kwok-cheung
    Kee, Chea-su
    OPTOMETRY AND VISION SCIENCE, 2015, 92 (05) : 604 - 614
  • [48] Mathematical modeling of a field emitter with a hyperbolic shape
    Egorov, N., V
    Vinogradova, E. M.
    VESTNIK SANKT-PETERBURGSKOGO UNIVERSITETA SERIYA 10 PRIKLADNAYA MATEMATIKA INFORMATIKA PROTSESSY UPRAVLENIYA, 2020, 16 (03): : 238 - 248
  • [49] On some mathematical models in nonlinear elasticity
    G. Prouse
    Journal of Mathematical Sciences, 1999, 93 (5) : 767 - 771
  • [50] MATHEMATICAL MODEL OF THE PART SHAPE AND AUTOMATION ON ITS BASIS OF THE PROCESS OF DEVELOPING THE DRAWING PARAMETERS OF THE AXISYMMETRIC FORGING
    Telegin, I. V.
    Telegin, V. V.
    TURKISH ONLINE JOURNAL OF DESIGN ART AND COMMUNICATION, 2018, 8 : 458 - 464
12345