TY - JOUR
T1 - A Monotone Domain Decomposition Algorithm for Solving Weighted Average Approximations to Nonlinear Singularly Perturbed Parabolic Problems
AU - Igor Boglaev & Matthew Hardy
JO - Journal of Computational Mathematics
VL - 1
SP - 76
EP - 97
PY - 2008
DA - 2008/02
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8612.html
KW - Parabolic reaction-diffusion problem, Boundary layers, $θ$-method, Monotone
domain decomposition algorithm, Uniform convergence.
AB - <p style="text-align: justify;">This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated. Numerical experiments are presented.</p>