A linearised singularly perturbed convection–diffusion problem with an interior layer

O’Riordan, Eugene; Quinn, Jason

doi:10.1016/j.apnum.2015.08.002

Cited by 11 publications

(1 citation statement)

References 8 publications

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“…The methods were used to solve singularly perturbed parabolic problems in which the coefficients are discontinuous in the space variable. O'Riordan and Quinn examined a linear time dependent singularly perturbed convection–diffusion problems, where the convective coefficient got interior layer; to design and analyze a monotone finite difference operator and a piecewise‐uniform Shishkin mesh. Gracia and O'Riordan constructed and analyzed a numerical method consisting on a monotone finite difference operator and piecewise uniform mesh.…”

Section: Introductionmentioning

confidence: 99%

A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer

Munyakazi

Patidar

Sayi

2019

Numerical Methods Partial

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The objective of this paper is to construct and analyze a fitted operator finite difference method (FOFDM) for the family of time-dependent singularly perturbed parabolic convection-diffusion problems. The solution to the problems we consider exhibits an interior layer due to the presence of a turning point. We first establish sharp bounds on the solution and its derivatives. Then, we discretize the time variable using the classical Euler method. This results in a system of singularly perturbed interior layer two-point boundary value problems. We propose a FOFDM to solve the system above. Through a rigorous error analysis, we show that the scheme is uniformly convergent of order one with respect to both time and space variables. Moreover, we apply Richardson extrapolation to enhance the accuracy and the order of convergence of the proposed scheme. Numerical investigations are carried out to demonstrate the efficacy and robustness of the scheme. KEYWORDS error bounds, finite difference methods, interior layer, singularly perturbed problems, uniform convergence 1 Numer Methods Partial Differential Eq. 2019;35:2407-2422. wileyonlinelibrary.com/journal/num

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Section: Introductionmentioning

confidence: 99%