Volume 2, Issue 1
Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term

R. Mythili Priyadharshini & N. Ramanujam

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 100-118.

Published online: 2009-02

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  • 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.

  • Keywords

Singular perturbation problem, piecewise uniform mesh, discrete derivative, discontinuous convection coefficient, Robin boundary conditions, discontinuous source term.

  • AMS Subject Headings

65L10, CR G1.7

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-100, author = {}, title = {Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {1}, pages = {100--118}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6018.html} }
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 -

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.

R. Mythili Priyadharshini & N. Ramanujam. (2020). Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term. Numerical Mathematics: Theory, Methods and Applications. 2 (1). 100-118. doi:
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