An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag

Sushree Priyadarshana () and Jugal Mohapatra ()
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Sushree Priyadarshana: National Institute of Technology Rourkela
Jugal Mohapatra: National Institute of Technology Rourkela

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1389-1408

Abstract: Abstract The objective of this work is to provide an efficient numerical scheme for solving singularly perturbed parabolic convection-diffusion problems with a large time lag having Robin-type boundary conditions. The implicit Euler scheme is used in the temporal direction on a uniform mesh. To handle the layer behavior caused due to the presence of perturbation parameter, the problem is solved using the upwind scheme on two layer-resolving meshes in the spatial direction. As the Shishkin mesh makes the order of convergence to one up to a logarithmic factor, in the spatial direction, the presence of this effect is prevented by the use of the Bakhvalov-Shishkin mesh. Further, the robustness of the scheme is tested over semi-linear time-lagged initial boundary value problems. Numerical outputs are presented in the form of tables and graphs to prove the parameter-uniform nature and robustness of the proposed scheme.

Keywords: Singular perturbation; Convection-diffusion problem; Time lag; Robin-type boundary condition; Semi-linear parabolic problem; 65M06; 65M12; 35K20; 35K58 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00445-8

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