A uniformly convergent quadratic B-spline based scheme for singularly perturbed degenerate parabolic problems

Satpal Singh, Devendra Kumar and Higinio Ramos

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 195, issue C, 88-106

Abstract: In this article, a numerical scheme is developed to solve singularly perturbed convection–diffusion type degenerate parabolic problems. The degenerative nature of the problem is due to the coefficient b(x,t)=b0(x,t)xp,p≥1 of the convection term. As the perturbation parameter approaches zero, the solution to this problem exhibits a parabolic boundary layer in the neighborhood of the left end side of the domain. The problem is semi-discretized using the Crank–Nicolson scheme, and then the quadratic spline basis functions are used to discretize the semi-discrete problem. A priori bounds for the solution (and its derivatives) of the continuous problem are given, which are necessary to analyze the error. A rigorous error analysis shows that the proposed method is boundary layer resolving and second-order parameter uniformly convergent. Some numerical experiments have been devised to support the theoretical findings and the effectiveness of the proposed scheme.

Keywords: Singularly perturbed problem; Degenerate parabolic problem; Boundary layer; Parameter-uniform; Exponentially graded mesh (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:195:y:2022:i:c:p:88-106

DOI: 10.1016/j.matcom.2021.12.026

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