TY - JOUR
T1 - Uniform Quadratic Convergence of a Monotone Weighted Average Method for Semilinear Singularly Perturbed Parabolic Problems
AU - Igor Boglaev
JO - Journal of Computational Mathematics
VL - 6
SP - 620
EP - 637
PY - 2013
DA - 2013/12
SN - 31
DO - http://doi.org/10.4208/jcm.1307-m4238
UR - https://global-sci.org/intro/article_detail/jcm/9757.html
KW - Semilinear parabolic problem, Singular perturbation, Weighted average scheme,
Monotone iterative method, Uniform convergence.
AB - <p style="text-align: justify;">This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.</p>