Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 100-118. Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term R. Mythili Priyadharshini 1, N. Ramanujam 1*1 Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024, Tamilnadu, India. Received 27 April 2008; Accepted (in revised version) 8 September 2008 Abstract In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An $\varepsilon$-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions. AMS subject classifications: 65L10, CR G1.7 Key words: Singular perturbation problem, piecewise uniform mesh, discrete derivative, discontinuous convection coefficient, Robin boundary conditions, discontinuous source term. *Corresponding author. Email: mythiliroy777@yahoo.co.in (R. M. Priyadharshini), matram2k3@yahoo.com (N. Ramanujam)