scholarly journals A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term

2007 ◽  
Vol 202 (2) ◽  
pp. 203-216 ◽  
Author(s):  
A. Tamilselvan ◽  
N. Ramanujam ◽  
V. Shanthi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Source Term ◽  
Coupled System ◽  
Second Order ◽  
Singularly Perturbed ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Discontinuous Source Term

High Accuracy Simulation for the Weakly Coupled System of Two Second Order Ordinary Differential Equations

2011 ◽  
Vol 467-469 ◽  
pp. 377-382
Author(s):  
Xin Cai
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Asymptotic Properties ◽  
Coupled System ◽  
Second Order ◽  
Third Order ◽  
Multi Scale ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Component Systems

Coupled system of two second order ordinary differential equations with small parameter was considered. This is a multi-scale system. The solution of the system will change rapidly near both sides of the boundary layer. The system was decomposed into several systems in order to have fourth order asymptotic decomposition firstly. The asymptotic properties of all these systems were discussed secondly. The third order numerical methods were constructed for left side and right side singular component systems thirdly. The error estimation for the system was given finally.

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