Corneal Curvature

This chapter analyzes boundary value ordinary differential equation (BVODE) model for the calculation of the cornea shape. The BVODE is derived by a static force balance on the cornea. A numerical procedure for the integration (solution) of the BVODE model is discussed. The general numerical procedure for the solution of the BVODEs is to add a pseudo derivative in an initial value variable t, thereby producing a PDE in (x, t) that can be integrated by the method of lines (MOL). The chapter talks about the R routines for the implementation of the numerical procedure. It discusses the numerical solution produced by the routines, including an assessment of the accuracy of the solution. The chapter further provides an introduction to initial values ordinary differential equations (IVODE), BVODE, and PDEs, all within a single application example.