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
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.
Email: firstname.lastname@example.org (R. M. Priyadharshini), email@example.com (N. Ramanujam)