A Numerical Scheme for Solving a Coupled System of Singularly Perturbed Delay Differential Equations of Reaction–Diffusion Type

2018 ◽  
pp. 305-312
Author(s):  
Trun Gupta ◽  
P. Pramod Chakravarthy
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Scheme ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Delay Differential

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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