scholarly journals ASYMPTOTIC-NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL DIFFERENCE EQUATIONS OF MIXED-TYPE

2015 ◽  
Vol 33 (5_6) ◽  
pp. 485-502
Author(s):  
A.A. SALAMA ◽  
D.G. AL-AMERY
Keyword(s):  
Numerical Method ◽  
Difference Equations ◽  
Mixed Type ◽  
Singularly Perturbed ◽  
Asymptotic Numerical Method ◽  
Equations Of Mixed Type

scholarly journals Center projections for smooth difference equations of mixed type

2008 ◽  
Vol 244 (4) ◽  
pp. 803-835 ◽  
Author(s):  
H.J. Hupkes ◽  
E. Augeraud-Véron ◽  
S.M. Verduyn Lunel
Keyword(s):  
Difference Equations ◽  
Mixed Type ◽  
Equations Of Mixed Type

scholarly journals Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Habtamu Garoma Debela ◽  
Solomon Bati Kejela ◽  
Ayana Deressa Negassa
Keyword(s):  
Numerical Method ◽  
Difference Equations ◽  
Oscillatory Behavior ◽  
Singularly Perturbed ◽  
Stability And Convergence ◽  
Uniform Mesh ◽  
Small Shift ◽  
Exponentially Fitted ◽  
Maximum Absolute Errors ◽  
The Stability

This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on four model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.

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