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AIMS Mathematics

2024, Volume 9, Issue 8: 22547-22564. doi: 10.3934/math.20241097
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Research article

Computational methods for singularly perturbed differential equations with advanced argument of convection-diffusion type

  • 1.
    Graduate Institute of Automation Technology, National Taipei University of Technology, Taipei 10608, Taiwan
  • 2.
    Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India
  • 3.
    Centre for Computational Modeling, Chennai Institute of Technology, Chennai-600 069, Tamilnadu, India
  • Received: 04 June 2024 Revised: 28 June 2024 Accepted: 16 July 2024 Published: 22 July 2024

  • MSC : 65L10, 65M15, 65N15

  • This study investigates singularly perturbed differential equations through advanced convection-diffusion techniques. We employ a finite difference approach utilizing a piecewise uniform Shishkin-type mesh to tackle this problem. Our analysis demonstrates that the approach achieves virtually first-order convergence. Error estimates are computed using discrete norms, and numerical experiments are conducted to validate these theoretical results.

    Citation: Nien-Tsu Hu, Sekar Elango, Chin-Sheng Chen, Murugesan Manigandan. Computational methods for singularly perturbed differential equations with advanced argument of convection-diffusion type[J]. AIMS Mathematics, 2024, 9(8): 22547-22564. doi: 10.3934/math.20241097

    Related Papers:

  • This study investigates singularly perturbed differential equations through advanced convection-diffusion techniques. We employ a finite difference approach utilizing a piecewise uniform Shishkin-type mesh to tackle this problem. Our analysis demonstrates that the approach achieves virtually first-order convergence. Error estimates are computed using discrete norms, and numerical experiments are conducted to validate these theoretical results.



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