TY - JOUR
T1 - A Uniformly Convergent Method on Arbitrary Meshes for a Semilinear Convection-Diffusion Problem with Discontinuous Data
AU - Boglaev , Igor
AU - Pack , Sophie
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 24
EP - 39
PY - 2008
DA - 2008/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/795.html
KW - convection-diffusion problem, discontinuous data, boundary layer, uniform convergence, monotone iterative method.
AB - <p style="text-align: justify;">This paper deals with a uniform (in a perturbation
parameter) convergent difference scheme for solving a nonlinear
singularly perturbed two-point boundary value problem with discontinuous
data of a convection-diffusion type. Construction of the difference
scheme is based on locally exact schemes or on local Green&#39;s functions.
Uniform convergence with first order of the proposed difference scheme
on arbitrary meshes is proven. A monotone iterative method, which is
based on the method of upper and lower solutions, is applied to
computing the nonlinear difference scheme. Numerical experiments are
presented.</p>