TY - JOUR
T1 - Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 22
PY - 2010
DA - 2010/03
SN - 3
DO - http://doi.org/10.4208/nmtma.2009.m8015
UR - https://global-sci.org/intro/article_detail/nmtma/5986.html
KW - Singular perturbation problems, delay differential equations, boundary layer, upwind
scheme, adaptive mesh, uniform convergence.
AB - <p style="text-align: justify;">Adaptive grid methods are established as valuable computational
technique in approximating effectively the solutions of problems
with boundary or interior layers. In this paper, we present the
analysis of an upwind scheme for singularly perturbed
differential-difference equation on a grid which is formed by
equidistributing arc-length monitor function. It is shown that the
discrete solution obtained converges uniformly with respect to
the perturbation parameter. Numerical experiments illustrate in
practice the result of convergence proved theoretically.</p>