Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one- and two-dimensional photonic crystals

2006 ◽  
Vol 23 (10) ◽  
pp. 2249 ◽  
Author(s):  
Alberto Mendoza-Suárez ◽  
Francisco Villa-Villa ◽  
Jorge A. Gaspar-Armenta
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
Numerical Method ◽  
Integral Equations ◽  
Two Dimensional

Band structure of absorptive two-dimensional photonic crystals

2003 ◽  
Vol 20 (6) ◽  
pp. 1334 ◽  
Author(s):  
Han van der Lem ◽  
Adriaan Tip ◽  
Alexander Moroz
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
Two Dimensional

Band structure calculation in two-dimensional Kerr-nonlinear photonic crystals

2005 ◽  
Vol 248 (4-6) ◽  
pp. 469-477 ◽  
Author(s):  
I.S. Maksymov ◽  
L.F. Marsal ◽  
M.A. Ustyantsev ◽  
J. Pallarès
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
Structure Calculation ◽  
Band Structure Calculation ◽  
Two Dimensional ◽  
Nonlinear Photonic Crystals

scholarly journals Numerical Solution for the 2D Linear Fredholm Functional Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Neda Khaksari ◽  
Mahmoud Paripour ◽  
Nasrin Karamikabir
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Unknown Function ◽  
Numerical Solutions ◽  
Functional Integral ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

In this work, a numerical method is applied for obtaining numerical solutions of Fredholm two-dimensional functional linear integral equations based on the radial basis function (RBF). To find the approximate solutions of these types of equations, first, we approximate the unknown function as a finite series in terms of basic functions. Then, by using the proposed method, we give a formula for determining the unknown function. Using this formula, we obtain a numerical method for solving Fredholm two-dimensional functional linear integral equations. Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.

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