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

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 f...

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Bibliographic Details
Published inJournal of Mathematics Vol. 2021; pp. 1 - 15
Main Authors Hammachukiattikul, P., Sekar, E., Tamilselvan, A., Vadivel, R., Gunasekaran, N., Agarwal, Praveen
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 04.06.2021
Hindawi Limited
John Wiley & Sons, Inc
Wiley
Subjects
Comparative studies
Decomposition
Differential equations
Finite difference method
Mathematical analysis
Mathematics
Methods
Numerical analysis
Numerical methods
QA1-939
Online AccessGet full text
ISSN2314-4629
2314-4785
DOI10.1155/2021/6636607

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Summary: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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ISSN:2314-4629
2314-4785
DOI:10.1155/2021/6636607