Second-Order Uniformly Convergent Richardson Extrapolation Method for Singularly Perturbed Degenerate Parabolic PDEs

2017 ◽  
Vol 3 (S1) ◽  
pp. 31-53 ◽  
Author(s):  
Anirban Majumdar ◽  
Srinivasan Natesan
Keyword(s):  
Richardson Extrapolation ◽  
Second Order ◽  
Singularly Perturbed ◽  
Extrapolation Method ◽  
Parabolic Pdes ◽  
Uniformly Convergent ◽  
Degenerate Parabolic ◽  
Richardson Extrapolation Method

ASSESSMENT OF RICHARDSON EXTRAPOLATION METHOD IN THE CFD MESH CONVERGENCE PROCESS

2016 ◽  
Author(s):  
Zilmara Zamyla da Silva Almeida ◽  
Yuri da Silva Pereira ◽  
Elmo de Sena Ferreira Júnior ◽  
Sávio Vianna
Keyword(s):  
Richardson Extrapolation ◽  
Extrapolation Method ◽  
Convergence Process ◽  
Richardson Extrapolation Method ◽  
Mesh Convergence

scholarly journals Uniform Hybrid Difference Scheme for Singularly Perturbed Differential-Difference Turning Point Problems Exhibiting Boundary Layers

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Wondwosen Gebeyaw Melesse ◽  
Awoke Andargie Tiruneh ◽  
Getachew Adamu Derese
Keyword(s):  
Difference Scheme ◽  
Boundary Layers ◽  
Turning Point ◽  
Original Problem ◽  
Second Order ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Uniformly Convergent ◽  
Theoretical Results ◽  
Taylor’S Series

In this paper, a class of linear second-order singularly perturbed differential-difference turning point problems with mixed shifts exhibiting two exponential boundary layers is considered. For the numerical treatment of these problems, first we employ a second-order Taylor’s series approximation on the terms containing shift parameters and obtain a modified singularly perturbed problem which approximates the original problem. Then a hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the modified problem. Further, we proved that the method is almost second-order ɛ-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results. In addition, the effect of the shift parameters on the layer behavior of the solution is also examined.

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