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Robust numerical analysis for 2D singularly perturbed elliptic delay differential equations exhibiting interior layers due to singularity propagation

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  • Garima,
  • Sharma, Kapil K.
  • Bansal, Komal

Abstract

The purpose of this work is to develop a numerical method and its robust convergence analysis for 2D elliptic delay differential equations. The elliptic problems have been considered with unit shifts in undifferentiated terms of both spatial directions resulting in interior layers. The exploration of 2D singularly perturbed elliptic reaction-diffusion delay differential equations exhibiting characteristics boundary and interior layers is a novel and unexplored area in the current scientific literature. In this work, the study of interior layers has been extended to the solution of the problems. A fitted mesh robust numerical method has been developed, which is almost second-order convergent up to the logarithmic factor. The numerical results have been included to demonstrate the singularity propagation in the layer behavior of the numerical solution due to delay arguments.

Suggested Citation

  • Garima, & Sharma, Kapil K. & Bansal, Komal, 2026. "Robust numerical analysis for 2D singularly perturbed elliptic delay differential equations exhibiting interior layers due to singularity propagation," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    • Handle: RePEc:eee:apmaco:v:512:y:2026:i:c:s0096300325004953
    DOI: 10.1016/j.amc.2025.129770
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    References listed on IDEAS

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    1. 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.
    2. Brdar, Mirjana & Franz, Sebastian & Ludwig, Lars & Roos, Hans-Görg, 2023. "A balanced norm error estimation for the time-dependent reaction-diffusion problem with shift in space," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    3. Sharma, Amit & Rai, Pratima, 2023. "Analysis of a higher order uniformly convergent method for singularly perturbed parabolic delay problems," Applied Mathematics and Computation, Elsevier, vol. 448(C).
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