TY - JOUR
T1 - An Almost Fourth Order Parameter-Robust Numerical Method for a Linear System of ($M\geq2$) Coupled Singularly Perturbed Reaction-Diffusion Problems
AU - Rao , S. C. S.
AU - Kumar , M.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 603
EP - 621
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/585.html
KW - Parameter-robust convergence, System of coupled reaction-diffusion problem, Generalized-Shishkin mesh, Fourth order compact difference scheme, Central difference scheme.
AB - <p style="text-align: justify;">We present a high order parameter-robust finite difference method for a linear system
of ($M\geq2$) coupled singularly perturbed reaction-diffusion two point boundary value problems.
The problem is discretized using a suitable combination of the fourth order compact difference
scheme and the central difference scheme on a generalized Shishkin mesh. A high order decomposition of the exact solution into its regular and singular parts is constructed. The error analysis is
given and the method is proved to have almost fourth order parameter robust convergence, in the
maximum norm. Numerical experiments are conducted to demonstrate the theoretical results.</p>