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An orthogonal spline collocation method for singularly perturbed parabolic reaction–diffusion problems with time delay

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Abstract

In this article, a numerical technique is developed and analyzed for singularly perturbed delay parabolic reaction–diffusion problems with Dirichlet boundary condition. An orthogonal spline collocation method with \(C^1\)-cubic spline basis functions on a Shishkin mesh is used in the spatial direction. In the temporal direction Crank–Nicolson method on an equidistant mesh is used. An extensive analysis has been undertaken to establish the uniform convergence with respect to the perturbation parameter. To support the theoretical findings, numerical experiments have been presented.

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Authors and Affiliations

  1. Department of Mathematics, South Asian University, New Delhi, 110068, India

    Jewel Howlader & Kapil K. Sharma

  2. Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi, 110019, India

    Pankaj Mishra

Authors
  1. Jewel Howlader
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  2. Pankaj Mishra
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  3. Kapil K. Sharma
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Correspondence to Kapil K. Sharma.

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Howlader, J., Mishra, P. & Sharma, K.K. An orthogonal spline collocation method for singularly perturbed parabolic reaction–diffusion problems with time delay. J. Appl. Math. Comput. 70, 1069–1101 (2024). https://doi.org/10.1007/s12190-024-01993-w

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