TY - JOUR
T1 -  Uniform Convergence via Preconditioning.
AU - RELJA VULANOVI  ́C AND TH  ́AI ANH NHAN
JO - International Journal of Numerical Analysis Modeling Series B
VL - 4
SP - 347
EP - 356
PY - 2014
DA - 2014/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/239.html
KW - singular perturbation
KW - convection-diffusion
KW - boundary-value problem
KW - Shishkin mesh
KW - finite differences
KW - uniform convergence
KW - preconditioning
AB - The linear singularly perturbed convection-diffusion problem in one dimension is
considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple
proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is
based on the preconditioning of the discrete system.