Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens
A. Yildirim1**, A. Gökdoğan2, M. Merdan3, V. Lakshminarayanan4,5
1Department of Mathematics, Zeytinalani University, 4146 Sk. No 16 Zeytinalani Mah. 35440 Urla-Izmir, Turkey 2Department of Mathematics Engineering, Gümü?hane University, 29100 Gümü?hane, Turkey 3Department of Mathematics Engineering, Gümü?hane University, 29100 Gümü?hane, Turkey 4School of Optometry and Departement of Physics and Electrical Engineering, University of Waterloo, Waterloo, Canada 5 Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, USA
Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens
A. Yildirim1**, A. Gökdoğan2, M. Merdan3, V. Lakshminarayanan4,5
1Department of Mathematics, Zeytinalani University, 4146 Sk. No 16 Zeytinalani Mah. 35440 Urla-Izmir, Turkey 2Department of Mathematics Engineering, Gümüşhane University, 29100 Gümüşhane, Turkey 3Department of Mathematics Engineering, Gümüşhane University, 29100 Gümüşhane, Turkey 4School of Optometry and Departement of Physics and Electrical Engineering, University of Waterloo, Waterloo, Canada 5 Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, USA
An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge–Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms.
An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge–Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms.
(Ordinary and partial differential equations; boundary value problems)
引用本文:
A. Yildirim, A. Gökdoğan, M. Merdan, V. Lakshminarayanan. Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens[J]. 中国物理快报, 2012, 29(7): 74202-074202.
A. Yildirim, A. Gökdoğan, M. Merdan, V. Lakshminarayanan. Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens. Chin. Phys. Lett., 2012, 29(7): 74202-074202.
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