TY - JOUR
T1 - Numerical Solutions of Nonlinear Parabolic Problems by Monotone Jacobi and Gauss-Seidel Methods
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 599
EP - 614
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/703.html
KW - Nonlinear parabolic problem, monotone iterative method, singularly perturbed problem, uniform convergence.
AB - <p style="text-align: justify;">This paper is concerned with solving nonlinear monotone difference
schemes of the parabolic type. The monotone Jacobi and monotone Gauss-Seidel methods are constructed. Convergence rates of the methods are compared
and estimated. The proposed methods are applied to solving nonlinear
singularly perturbed parabolic problems. Uniform convergence of the monotone
methods is proved. Numerical experiments complement the theoretical
results.</p>