Roos, H.-G.; Stynes, M.; Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion and Flow Problems. Berlin etc., Springer-Verlag 1996. XVI, 348 pp., DM 148,00. ISBN 3-540-60718-8 (Springer Series in Computational Mathematics 24)

1997 ◽  
Vol 77 (5) ◽  
pp. 403-403
Author(s):  
G. I. Shishkin
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Singularly Perturbed ◽  
Computational Mathematics ◽  
Convection Diffusion ◽  
Flow Problems ◽  
Springer Series

scholarly journals Robust Numerical Methods for Singularly Perturbed Differential Equations: A Survey Covering 2008–2012

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Hans-Görg Roos
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Differential Equations ◽  
Adaptive Methods ◽  
Singularly Perturbed ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Stabilization Methods ◽  
Singularly Perturbed Equations

We present new results in the numerical analysis of singularly perturbed convection-diffusion-reaction problems that have appeared in the last five years. Mainly discussing layer-adapted meshes, we present also a survey on stabilization methods, adaptive methods, and on systems of singularly perturbed equations.

scholarly journals Note on the Sensitivity of Simulated Solutions of the Nonlinear Singularly Perturbed Dynamical System on the Used Different Rewriting into a System of First Order Differential Equations

2016 ◽  
Vol 24 (39) ◽  
pp. 51-55
Author(s):  
Vladimír Liška ◽  
Zuzana Šútova ◽  
Dušan Pavliak
Keyword(s):  
Dynamical System ◽  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Numerical Scheme ◽  
Singularly Perturbed ◽  
First Order ◽  
First Order Differential Equations

Abstract In this paper we analyze the sensitivity of solutions to a nonlinear singularly perturbed dynamical system based on different rewriting into a System of the First Order Differential Equations to a numerical scheme. Numerical simulations of the solutions use numerical methods implemented in MATLAB.

scholarly journals Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
P. Hammachukiattikul ◽  
E. Sekar ◽  
A. Tamilselvan ◽  
R. Vadivel ◽  
N. Gunasekaran ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Discrete Norm ◽  
Difference Methods ◽  
Second Order Convergence ◽  
Delay Differential

In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20).

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