A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems

By Niall Madden, Martin Stynes. 2003

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The Sdfem for a Convection-diffusion Problem with Two Small Parameters (2003, unknown): “While Stynes and Tobiska use the consistency error of the difference scheme generated by the SDFEM, our approach uses mainly finite element tools.”
A uniformly convergent scheme for a system of reaction-diffusion equations (2007, background): “Taking into account that | w/ t | B 2(x) C, the same argument as in [11] proves∣∣∣ w1 x (x, t) ∣∣∣ C −1/2 1 B 2(x), ∣∣∣ w1 x2 (x, t) ∣∣∣ C −1 1 B 2(x), (22)”
A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations (2004, methodology): “Parameter-robust numerical methods for a system of singularly perturbed reactiondiffusion ordinary differential equations have been examined by [13, 6, 7].”
A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term (2007, methodology): “available in the literature in order to obtain numerical solution to singularly perturbed system of second order differential equations subject to Dirichlet type boundary conditions when source terms are smooth on [5,2,3,6,7].”