TY - JOUR
T1 - Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 100
EP - 118
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6018.html
KW - Singular perturbation problem, piecewise uniform mesh, discrete derivative, discontinuous convection coefficient, Robin boundary conditions, discontinuous source term.
AB - <p style="text-align: justify;">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.</p>