@Article{AAMM-6-637,
author = {Hsieh , Po-WenYang , Suh-Yuh and You , Cheng-Shu},
title = {A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2014},
volume = {6},
number = {5},
pages = {637--662},
abstract = {<p style="text-align: justify;">This paper is devoted to a new high-accuracy finite difference
scheme for solving reaction-convection-diffusion problems
with a small diffusivity $\varepsilon$.
With a novel treatment for the reaction term, we first derive a difference scheme
of accuracy $\mathcal{O}(\varepsilon^2 h + \varepsilon h^2 + h^3)$ for the 1-D case.
Using the alternating direction technique, we then extend the scheme
to the 2-D case on a nine-point stencil.
We apply the high-accuracy finite difference scheme to solve the 2-D steady
incompressible Navier-Stokes equations in the stream function-vorticity formulation.
Numerical examples are given to illustrate the effectiveness
of the proposed difference scheme.
Comparisons made with some high-order compact difference schemes
show that the newly proposed scheme can achieve good accuracy
with better stability.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.5.s4},
url = {http://global-sci.org/intro/article_detail/aamm/40.html}
}