Orthogonal grid generation of an irregular region using a local polynomial collocation method

2013 ◽  
Vol 243 ◽  
pp. 58-73 ◽  
Author(s):  
Nan-Jing Wu ◽  
Ting-Kuei Tsay ◽  
Tun-Chi Yang ◽  
Hung-Yuan Chang
Keyword(s):  
Collocation Method ◽  
Grid Generation ◽  
Local Polynomial ◽  
Irregular Region ◽  
Orthogonal Grid ◽  
Polynomial Collocation

scholarly journals Piecewise Legendre spectral-collocation method for Volterra integro-differential equations

2015 ◽  
Vol 18 (1) ◽  
pp. 231-249 ◽  
Author(s):  
Zhendong Gu ◽  
Yanping Chen
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Piecewise Polynomial ◽  
Spectral Collocation ◽  
Numerical Errors ◽  
Piecewise Polynomial Collocation Method ◽  
Theoretical Results ◽  
Polynomial Collocation ◽  
Better Than

Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in$h^{m}N^{-m}$-version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.

Quasi-K-Orthogonal Grid Generation

2019 ◽  
Author(s):  
Shahid Manzoor ◽  
Michael G. Edwards ◽  
Ali H. Dogru
Keyword(s):  
Grid Generation ◽  
Orthogonal Grid
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