TY - JOUR
T1 - Second Order Uniform Approximations for the Solution of Time Dependent Singularly Perturbed Reaction-Diffusion Systems
AU - C. Clavero, J. L. Gracia & F. Lisbona
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 428
EP - 443
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/729.html
KW - Reaction-diffusion problems, uniform convergence, coupled system, Shishkin mesh, second order.
AB - <p style="text-align: justify;">In this work we consider a parabolic system of two linear singularly
perturbed equations of reaction-diffusion type coupled in the reaction terms. To
obtain an efficient approximation of the exact solution we propose a numerical
method combining the Crank-Nicolson method used in conjunction with the
central finite difference scheme defined on a piecewise uniform Shishkin mesh.
The method gives uniform numerical approximations of second order in time
and almost second order in space. Some numerical experiments are given to
support the theoretical results.</p>