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Priyadharshini, R. Mythili; Ramanujam, N.; Shanthi, V.

Approximation of derivative in a system of singularly perturbed convection-diffusion equations. (English) Zbl 1182.65124

J. Appl. Math. Comput. 29, No. 1-2, 137-151 (2009).
It is embarrassing to write a review of this paper, since it was published twice by the same journal. Precisely: 7mm
A)
R. M. Priyandharshini, N. Ramanujam and V. Shanthi, “Approximation of derivative in a system of singularly perturbed convection-diffusion equations”, J. Appl. Math. Comput. 29, No. 1–2, 137–151 (2009; Zbl 1182.65124),
B)
R. M. Priyandharshini, N. Ramanujam and V. Shanthi, “Approximation of derivative in a system of singularly perturbed convection-diffusion equations”, J. Appl. Math. Comput. 30, No. 1–2, 369–383 (2009; Zbl 1182.65123).
The differences between these papers are essentially Acknowledgements, biographical notes and position of Figures and Tables. Actually, authors, title, abstract, theorems, lemmas and text words absolutely coincide. The papers deal with a weakly coupled system of two singularly perturbed convection-diffusion ordinary differential equations of second order. A standard second-order finite difference scheme on a piecewise uniform mesh is used to approximate the solution. Convergence is proved independently of perturbation parameter.
Since papers A) and B) are really the same paper and the reviewer was asked to review both of them, even reviews are duplicated.
Reviewer: Raffaella Pavani (Milano)

Cited in 2 Reviews
Cited in 6 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations

Keywords:

singular perturbation; piecewise uniform meshes; convection-diffusion equations; system; second-order finite difference scheme; convergence

Citations:

Zbl 1182.65123; Zbl 1182.65124
Cite Review PDF
Full Text: DOI

References:

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[15] Mythili Priyadharshini, R., Ramanujam, N.: Approximation of derivative for a singularly perturbed second-order ordinary differential equation of Robin type with discontinuous convection coefficient and source term. Accepted for publication in the Int. J. Numer. Math. · Zbl 1199.65249
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