Computational techniques for singularly perturbed reaction-diffusion delay differential equations: a second-order approach

Volume 35, Issue 3, pp 304--318 https://dx.doi.org/10.22436/jmcs.035.03.04

Publication Date: May 22, 2024 Submission Date: March 20, 2024 Revision Date: April 11, 2024 Accteptance Date: April 26, 2024

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Authors

D. Joy - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India. D. Kumar S - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India.

Abstract

For the analysis of singularly perturbed delay differential equations exhibiting layer or oscillatory behaviour and a slight negative shift in the reaction term, this study introduces a second order numerical approach via Stormer’s method. To approximate the term with negative shift, we use Taylor series, which in turn changes the equation into a singular perturbation problem with the same asymptotic behaviour. Finally, we have a recurrence relation with five terms that can be resolved using the Gauss elimination method. The computational results are shown by solving some model problems for different delay and perturbation parameters. The rate of convergence, both theoretically and numerically, has been demonstrated and is compatible with the present approach. The findings acquired using the new approach are shown to be more accurate than those obtained using the earlier investigations.

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Keywords

• Singular perturbation problems
• delay differential equations
• Stormer's method
• numerical methods

MSC

•  65L06
•  65L11
•  65L20
•  65L50

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