A Deferred Correction Approach to the Solution of Singularly Perturbed BVPs by High Order Upwind Methods: Implementation Details

2009 ◽  
Author(s):  
Pierluigi Amodio ◽  
Giuseppina Settanni ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
High Order ◽  
Singularly Perturbed ◽  
Deferred Correction ◽  
Upwind Methods

On the existence and evaluation of Stokes phenomena in fluid mechanics

2021 ◽  
pp. 1-27
Author(s):  
Nik Alexandrakis
Keyword(s):  
Fluid Mechanics ◽  
Simple Proof ◽  
Travelling Waves ◽  
High Order ◽  
Singularly Perturbed ◽  
Type Model ◽  
Underlying Theory ◽  
Stokes Constant ◽  
Splitting Constant ◽  
Stokes Phenomena

A singularly perturbed, high order KdV-type model, which describes localized travelling waves (“solitons”) is being considered. We focus on the Inner solution, and detect Stokes phenomena that are crucial as to whether we can obtain a suitable solution. We provide a simple proof that the corresponding Stokes constant is non-zero. Also, we evaluate this splitting constant numerically by using two methods that are induced by the underlying theory.

Simulation of a Steady-State Electron Shock Wave in a Submicron Semiconductor Device Using High-Order Upwind Methods

1991 ◽  
pp. 27-32 ◽  
Author(s):  
Emad Fatemi ◽  
Carl L. Gardner ◽  
Joseph W. Jerome ◽  
Stanley Osher ◽  
Donald J. Rose
Keyword(s):  
Shock Wave ◽  
Steady State ◽  
Semiconductor Device ◽  
High Order ◽  
State Electron ◽  
Upwind Methods

scholarly journals Integral deferred correction methods constructed with high order Runge–Kutta integrators

2009 ◽  
Vol 79 (270) ◽  
pp. 761-783 ◽  
Author(s):  
Andrew Christlieb ◽  
Benjamin Ong ◽  
Jing-Mei Qiu
Keyword(s):  
High Order ◽  
Deferred Correction ◽  
Runge Kutta
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