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Numerical solution of a time dependent singularly perturbed delay differential equation on an exponentially graded mesh

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  • P. Pramod Chakravarthy

    (Visvesvaraya National Institute of Technology)

  • Meenakshi Shivhare

    (Presidency University)

Abstract

In this article, we consider a singularly perturbed time-dependent reaction-diffusion problem with a large delay in space direction. The problem possess two boundary layers and also an interior layer. To find the numerical solution, we proposed a method which is comprised of an implicit Euler method in the time direction and a finite difference scheme on the exponentially graded mesh. The term containing the delay is treated using the theory of interpolation. The numerical method is shown to be first order parameter uniform convergent in space and time directions in the maximum norm. Theoretical estimates support the obtained numerical results.

Suggested Citation

  • P. Pramod Chakravarthy & Meenakshi Shivhare, 2024. "Numerical solution of a time dependent singularly perturbed delay differential equation on an exponentially graded mesh," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(4), pages 1329-1349, December.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:4:d:10.1007_s13226-023-00442-x
    DOI: 10.1007/s13226-023-00442-x
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