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

V. Subburayan and S. Natesan ()
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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

Mathematics, 2022, vol. 10, issue 18, 1-19

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.

Keywords: delay differential equations; 2D parabolic equations; fractional step method; convection diffusion problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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