scholarly journals An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

2003 ◽  
Vol 21 (10) ◽  
pp. 2284-2296 ◽  
Author(s):  
Chia-Chien Huang ◽  
Chia-Chih Huang ◽  
Jaw-Yen Yang
Keyword(s):  
Refractive Index ◽  
Domain Decomposition ◽  
Collocation Method ◽  
Efficient Method ◽  
Optical Waveguides ◽  
Spectral Collocation Method ◽  
Spectral Collocation

A Domain Decomposition Based Spectral Collocation Method for Lane-Emden Equations

2017 ◽  
Vol 22 (2) ◽  
pp. 542-571 ◽  
Author(s):  
Yuling Guo ◽  
Jianguo Huang
Keyword(s):  
Domain Decomposition ◽  
Collocation Method ◽  
Numerical Experiments ◽  
Computational Cost ◽  
Mathematical Physics ◽  
Spectral Collocation Method ◽  
Spectral Accuracy ◽  
Spectral Collocation ◽  
Numerical Performance

AbstractA domain decomposition based spectral collocation method is proposed for numerically solving Lane-Emden equations, which are frequently encountered in mathematical physics and astrophysics. Compared with the existing methods, this method requires less computational cost and is particularly suitable for long-term computation. The related error estimates are also established, indicating the spectral accuracy of the method. The numerical performance and efficiency of the method are illustrated by several numerical experiments.

Parametric Study of Simultaneous Radiative Transfer in Plane-Parallel Scattering Medium With Variable Refractive Index by Spectral Collocation Method

2013 ◽  
Author(s):  
Jing Ma ◽  
Yasong Sun ◽  
Benwen Li
Keyword(s):  
Refractive Index ◽  
Radiative Transfer ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Scattering Medium ◽  
Spectral Collocation ◽  
Plane Parallel ◽  
Derivative Term ◽  
Scattering Phase Function ◽  
Angular Domains

In this work, a spectral collocation method is developed to simulate radiative transfer in a refractive planar medium. The space and angular domains of radiative intensity are discretized by Chebyshev polynomials, and the angular derivative term and the integral term of radiative transfer equation are approximated by spectral collocation method. The spectral collocation method can provide exponential convergence and obtain high accuracy even using few nodes. There is a very satisfying correspondence between the spectral collocation results and available data in literatures. Influence of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the emissivity of boundary are investigated for the plane-parallel scattering medium with variable refractive index.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

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