Optical waveguide analysis using a Yee-lattice-based modified finite-difference formula for an arbitrary dielectric interface

2002 ◽  
Vol 85 (12) ◽  
pp. 1-9
Author(s):  
Takashi Ando ◽  
Hiroki Nakayama ◽  
Junji Yamauchi ◽  
Hisamatsu Nakano
Keyword(s):  
Finite Difference ◽  
Optical Waveguide ◽  
Dielectric Interface ◽  
Difference Formula

scholarly journals THE NUMERICAL TREATMENT OF NONLINEAR FRACTAL–FRACTIONAL 2D EMDEN–FOWLER EQUATION UTILIZING 2D CHELYSHKOV POLYNOMIALS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040042
Author(s):  
M. HOSSEININIA ◽  
M. H. HEYDARI ◽  
Z. AVAZZADEH
Keyword(s):  
Approximate Solution ◽  
Finite Difference ◽  
Test Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Time Step ◽  
Discrete Method ◽  
Difference Formula ◽  
Fowler Equation ◽  
Chelyshkov Polynomials

This paper develops an effective semi-discrete method based on the 2D Chelyshkov polynomials (CPs) to provide an approximate solution of the fractal–fractional nonlinear Emden–Fowler equation. In this model, the fractal–fractional derivative in the concept of Atangana–Riemann–Liouville is considered. The proposed algorithm first discretizes the fractal–fractional differentiation by using the finite difference formula in the time direction. Then, it simplifies the original equation to the recurrent equations by expanding the unknown solution in terms of the 2D CPs and using the [Formula: see text]-weighted finite difference scheme. The differentiation operational matrices and the collocation method play an important role to obtaining a linear system of algebraic equations. Last, solving the obtained system provides an approximate solution in each time step. The validity of the formulated method is investigated through a sufficient number of test problems.

Proposing and Validation of a New Four-Point Finite-Difference Formula With Manipulator Application

2018 ◽  
Vol 14 (4) ◽  
pp. 1323-1333 ◽  
Author(s):  
Yang Shi ◽  
Binbin Qiu ◽  
Dechao Chen ◽  
Jian Li ◽  
Yunong Zhang
Keyword(s):  
Finite Difference ◽  
Difference Formula

Finite-Difference Time-Domain Analysis on Nonlinear Fabry-Perot Resonator in Optical Waveguide Geometry

2001 ◽  
Vol 40 (Part 1, No. 4A) ◽  
pp. 2259-2263
Author(s):  
Masamitsu Fujii ◽  
Toshihiro Okamoto ◽  
Masanobu Haraguchi ◽  
Masuo Fukui ◽  
Samir J. Al-Bader
Keyword(s):  
Finite Difference ◽  
Optical Waveguide ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Fabry Perot ◽  
Difference Time ◽  
Waveguide Geometry
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