TY - JOUR
T1 - Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems
AU - Vulanović , Relja
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 235
EP - 244
PY - 2008
DA - 2008/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6050.html
KW - Boundary-value problem, singular perturbation, finite differences, Bakhvalov and piecewise equidistant meshes, $L^1$ stability.
AB - <p style="text-align: justify;">The paper is concerned with strongly nonlinear singularly perturbed boundary value problems in one dimension. The problems are solved numerically by finite-difference schemes on special meshes which are dense in the boundary layers. The
Bakhvalov mesh and a special piecewise equidistant mesh are analyzed. For the central
scheme, error estimates are derived in a discrete $L^1$ norm. They are of second order
and decrease together with the perturbation parameter&nbsp;ε. The fourth-order Numerov
scheme and the Shishkin mesh are also tested numerically. Numerical results show&nbsp;ε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.</p>