An Adaptive Mesh Selection Strategy for Solving Singularly Perturbed Parabolic Partial Differential Equations with a Small Delay

  • Kamalesh Kumar
  • Trun Gupta
  • P. Pramod Chakravarthy
  • R. Nageshwar RaoEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


In this paper, an adaptive mesh has been generated using the concept of entropy function for solving convection-diffusion singularly perturbed parabolic partial differential equations with a small delay. Similar problems are associated with a furnace used to process a metal sheet in control theory. The beauty of the method is, unlike the popular adaptive meshes (Bakhvalov and Shishkin), prior information of the width and position of the layers are not required. The method is independent of perturbation parameter ε and gives us an oscillation-free solution, without any user-introduced parameters. The applicability of the proposed method is illustrated by means of two examples.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kamalesh Kumar
    • 1
  • Trun Gupta
    • 1
  • P. Pramod Chakravarthy
    • 1
  • R. Nageshwar Rao
    • 2
    Email author
  1. 1.Department of MathematicsVisvesvaraya National Institute of TechnologyNagpurIndia
  2. 2.Vellore Institute of TechnologyVelloreIndia

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