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Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space

Author

Listed:
  • V. Subburayan

    (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India)

  • S. Natesan

    (Department of Mathematics, Indian Institute of Technology, Guwahati 781039, Assam, India)

Abstract

Singularly perturbed 2D parabolic delay differential equations with the discontinuous source term and convection coefficient are taken into consideration in this paper. For the time derivative, we use the fractional implicit Euler method, followed by the fitted finite difference method with bilinear interpolation for locally one-dimensional problems. The proposed method is shown to be almost first-order convergent in the spatial direction and first-order convergent in the temporal direction. Theoretical results are illustrated with numerical examples.

Suggested Citation

  • V. Subburayan & S. Natesan, 2022. "Parameter Uniform Numerical Method for Singularly Perturbed 2D Parabolic PDE with Shift in Space," Mathematics, MDPI, vol. 10(18), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3310-:d:912973
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    References listed on IDEAS

    as
    1. V. Subburayan & N. Ramanujam, 2013. "An Initial Value Technique for Singularly Perturbed Convection–Diffusion Problems with a Negative Shift," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 234-250, July.
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