Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SINGULAR PERTURBATIONS AND SMALL DELAYS THROUGH LIOUVILLE'S GREEN TRANSFORMATION

  • DANY JOY (Department of Mathematics, Vellore Institute of Technology) ;
  • DINESH KUMAR S (Department of Mathematics, Vellore Institute of Technology)
  • Received : 2024.04.06
  • Accepted : 2024.06.11
  • Published : 2024.09.30
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Abstract

In this paper, we introduce a numerical method for solving singularly perturbed delay differential equation using Liouville - Green transformation. As an initial step, we transformed the statement equation into a singular perturbation problem with boundary conditions and then we used Liouville - Green transformation to solve it. Almost second-order accuracy is achieved with the scheme derived. The algorithm's performance is assessed through the examination of multiple test scenarios that involve different perturbation settings and delay parameters. The results of the proposed method are compared with those of other numerical techniques already available. The numerical scheme is described together with error estimates and a convergence rate.

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References

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