A robust computational technique for a system of singularly perturbed reaction–diffusion equations
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References
- Bawa, R.K., Lal, A.K. and Kumar, V. (2011). An ε-uniform hybrid scheme for singularly perturbed delay differential equations, Applied Mathematics and Computation217(21): 8216–8222.
- Das, P. and Natesan, S. (2013). A uniformly convergent hybrid scheme for singularly perturbed system of reaction–diffusion Robin type boundary-value problems, Journal of Applied Mathematics and Computing41(1): 447–471.
- Doolan, E.P., Miller, J.J.H. and Schilders, W.H.A. (1980). Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin.
- Farrell, P.E., Hegarty, A.F., Miller, J.J.H., O’Riordan, E. and Shishkin, G.I. (2000). Robust Computational Techniques for Boundary Layers, Chapman & Hall/CRC Press, New York, NY.
- Madden, N. and Stynes, M. (2003). A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems, IMA Journal of Numerical Analysis23(4): 627–644.
- Matthews, S., Miller, J.J.H., O’Riordan, E. and Shishkin, G.I. (2000). Parameter-robust numerical methods for a system of reaction–diffusion problems with boundary layers, in G.I. Shishkin, J.J.H. Miller and L. Vulkov (Eds.), Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems, Nova Science Publishers, New York, NY, pp. 219–224.
- Matthews, S., O’Riordan, E. and Shishkin, G.I. (2002). A numerical method for a system of singularly perturbed reaction–diffusion equations, Journal of Computational and Applied Mathematics145(1): 151–166.
- Melenk, J.M., Xenophontos, C. and Oberbroeckling, L. (2013). Analytic regularity for a singularly perturbed system of reaction–diffusion equations with multiple scales, Advances in Computational Mathematics39(2): 367–394.
- Miller, J.J.H., O’Riordan, E. and Shishkin, G.I. (1996). Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore.
- Natesan, S. and Briti, S.D. (2007). A robust computational method for singularly perturbed coupled system of reaction–diffusion boundary value problems, Applied Mathematics and Computation188(1): 353–364.
- Nayfeh, A.H. (1981). Introduction to Perturbation Methods, Wiley, New York, NY.
- Rao, S.C.S., Kumar, S. and Kumar, M. (2011). Uniform global convergence of a hybrid scheme for singularly perturbed reaction–diffusion systems, Journal of Optimization Theory and Applications151(2): 338–352.
- Roos, H.-G., Stynes, M. and Tobiska, L. (1996). Numerical Methods for Singularly Perturbed Differential Equations, Springer, Berlin.
- Shishkin, G.I. (1995). Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations, Computational Mathematics and Mathematical Physics35(4): 429–446.
- Sun, G. and Stynes, M. (1995). An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction–diffusion problem, Numerische Mathematik70(4): 487–500.
- Valanarasu, T. and Ramanujam, N. (2004). An asymptotic initial-value method for boundary value problems for a system of singularly perturbed second-order ordinary differential equations, Applied Mathematics and Computation147(1): 227–240.
Language: English
Page range: 387 - 395
Submitted on: Mar 7, 2013
Published on: Jun 26, 2014
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
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© 2014 Vinod Kumar, Rajesh K. Bawa, Arvind K. Lal, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.