Approximation of derivative in a system of singularly perturbed convection-diffusion equations. (English) Zbl 1182.65124
It is embarrassing to write a review of this paper, since it was published twice by the same journal. Precisely:
7mm
Since papers A) and B) are really the same paper and the reviewer was asked to review both of them, even reviews are duplicated.
- 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).
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)
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; convergenceReferences:
[1] | Bellew, S., O’Riordan, E.: A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations. Appl. Numer. Math. 51(2–3), 171–186 (2004) · Zbl 1059.65063 · doi:10.1016/j.apnum.2004.05.006 |
[2] | Cen, Z.: Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection-diffusion equations. Int. J. Comput. Math. 82(2), 177–192 (2005) · Zbl 1068.65101 · doi:10.1080/0020716042000301798 |
[3] | Cen, Z.: Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection-diffusion equations. J. Syst. Sci. Complex. 18(4), 498–510 (2005) · Zbl 1087.65072 |
[4] | Doolan, E.P., Miller, J.J.H., Schilders, W.H.A.: Uniform numerical methods for problems with initial and boundary layers. Boolen Press, Dublin (1980) · Zbl 0459.65058 |
[5] | Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Robust Computational Techniques for Boundary Layers. Chapman and Hall/CRC Press, Boca Raton (2000) · Zbl 0964.65083 |
[6] | Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Singularly perturbed convection- diffusion problem with boundary and weak interior layers. J. Comput. Appl. Math. 166(1), 133–151 (2004) · Zbl 1041.65059 · doi:10.1016/j.cam.2003.09.033 |
[7] | Fröhner, A., Linß, T., Roos, H.G.: Defect correction on Shiskin-type meshes. Numer. Algorithms 26(3), 281–299 (2001) · Zbl 0976.65074 · doi:10.1023/A:1016664926018 |
[8] | Kopteva, N., Stynes, M.: Approximation of derivatives in a convection-diffusion two-point boundary value problem. Appl. Numer. Math. 39(1), 47–60 (2001) · Zbl 0987.65069 · doi:10.1016/S0168-9274(01)00051-4 |
[9] | Linß, T.: On system of singularly perturbed reaction-convection-diffusion equations. Preprint MATH-NM-10-2006, TU Dresden, July 2006 |
[10] | Linß, T.: Analysis of an upwind finite difference scheme for a system of coupled singularly perturbed convection-diffusion equations. Preprint MATH-NM-08-2006, TU Dresden, July 2006 |
[11] | Madden, N., Stynes, M.: A uniform convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problem. IMA J. Numer. Anal. 23(4), 627–644 (2003) · Zbl 1048.65076 · doi:10.1093/imanum/23.4.627 |
[12] | Mathews, S., O’Riordan, E., Shishkin, G.I.: A numerical method for a system of singularly perturbed reaction-diffusion equations. J. Comput. Appl. Math. 145(1), 151–166 (2002) · Zbl 1004.65079 · doi:10.1016/S0377-0427(01)00541-6 |
[13] | Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Fitted Numerical Methods for Singular Perturbation Problems. World Scientific, Singapore (1996) |
[14] | Mythili Priyadharshini, R., Ramanujam, N.: Approximation of derivative to a singularly perturbed second-order ordinary differential equation with discontinuous convection coefficient using hybrid difference scheme. Communicated · Zbl 1170.65067 |
[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 |
[16] | Shanthi, V., Ramanujam, N.: A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations. Appl. Math. Comput. 47, 1673–1688 (2004) · Zbl 1070.65065 · doi:10.1016/j.camwa.2004.06.015 |
[17] | Tamilselvan, A., Ramanujam, N., Shanthi, V.: A numerical methods for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term. J. Comput. Appl. Math. 202, 203–216 (2007) · Zbl 1115.65086 · doi:10.1016/j.cam.2006.02.025 |
[18] | Valanarasu, T., Ramanujam, N.: An asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations. Appl. Math. Comput. 147, 227–240 (2004) · Zbl 1040.65071 · doi:10.1016/S0096-3003(02)00663-X |
[19] | Valarmathi, S., Ramanujam, N.: A computational method for solving boundary value problems for singularly perturbed third-order ordinary differential equations. Int. J. Comput. Math. 81(1–2) (2001) · Zbl 1025.65045 |
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