TY - JOUR
T1 - Monotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems. 
AU - IGOR BOGLAEV
JO - International Journal of Numerical Analysis Modeling Series B
VL - 4
SP - 402
EP - 414
PY - 2011
DA - 2011/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/320.html
KW - semilinear elliptic problem
KW - monotone difference schemes
KW - monotone relaxation iterates
KW - singularly perturbed problems
KW - uniform convergence
AB - This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone &#969-Jacobi and SUR (Successive Under-Relaxation)
methods are constructed. The monotone methods solve only linear discrete systems at each iterative
step and converge monotonically to the exact solution of the nonlinear monotone difference
schemes. Convergent rates of the monotone methods are estimated. The proposed methods are
applied to solving semilinear singularly perturbed reaction-diffusion problems. Uniform convergence
of the monotone methods is proved. Numerical experiments complement the theoretical
results.