@Article{IJNAM-10-178,
author = {V. Franklin, M. Paramasivam, J.J.H. Miller and S. Valarmathi},
title = {Second Order Parameter-Uniform Convergence for a Finite Difference Method for a Singularly Perturbed Linear Parabolic System},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {1},
pages = {178--202},
abstract = {<p style="text-align: justify;">A singularly perturbed linear system of second order partial differential
equations of parabolic reaction-diffusion type with given initial and
boundary conditions is considered. The diffusion term of each equation is multiplied
by a small positive parameter. These singular perturbation parameters
are assumed to be distinct. The components of the solution exhibit overlapping
layers. Shishkin piecewise-uniform meshes are introduced, which are used
in conjunction with a classical finite difference discretisation, to construct a
numerical method for solving this problem. It is proved that in the maximum
norm the numerical approximations obtained with this method are first order
convergent in time and essentially second order convergent in the space
variable, uniformly with respect to all of the parameters.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/564.html}
}