A robust computational technique for a system of singularly perturbed reaction–diffusion equations

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): 8216–8222.10.1016/j.amc.2011.02.089Search in Google Scholar

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): 447–471.10.1007/s12190-012-0611-7Search in Google Scholar

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.Search in Google Scholar

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.10.1201/9781482285727Search in Google Scholar

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): 627–644.10.1093/imanum/23.4.627Search in Google Scholar

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.Search in Google Scholar

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): 151–166.10.1016/S0377-0427(01)00541-6Search in Google Scholar

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): 367–394.10.1007/s10444-012-9284-xSearch in Google Scholar

Miller, J.J.H., O’Riordan, E. and Shishkin, G.I. (1996). Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore.10.1142/2933Search in Google Scholar

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): 353–364.10.1016/j.amc.2006.09.120Search in Google Scholar

Nayfeh, A.H. (1981). Introduction to Perturbation Methods, Wiley, New York, NY.Search in Google Scholar

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): 338–352.10.1007/s10957-011-9867-6Search in Google Scholar

Roos, H.-G., Stynes, M. and Tobiska, L. (1996). Numerical Methods for Singularly Perturbed Differential Equations, Springer, Berlin.10.1007/978-3-662-03206-0Search in Google Scholar

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.Search in Google Scholar

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): 487–500.10.1007/s002110050130Search in Google Scholar

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): 227–240.10.1016/S0096-3003(02)00663-XSearch in Google Scholar