Monotone Iterates with Quadratic Convergence Rate for Solving Semilinear Parabolic Problems.
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@Article{IJNAMB-2-109,
author = {Igor Boglaev},
title = {Monotone Iterates with Quadratic Convergence Rate for Solving Semilinear Parabolic Problems.},
journal = {International Journal of Numerical Analysis Modeling Series B},
year = {2011},
volume = {2},
number = {2},
pages = {109--123},
abstract = {This paper deals with numerical solving semilinear parabolic problems based on the
method of upper and lower solutions. A monotone iterative method with quadratic convergence
rate is constructed. The monotone iterative method combines an explicit construction of initial
upper and lower solutions and the modified accelerated monotone iterative method. The monotone
iterative method leads to the existence-uniqueness theorem. An analysis of convergence rates of
the monotone iterative method, based on different stoping tests, is given. Results of numerical
experiments are presented, where iteration counts are compared with a monotone iterative method,
whose convergence rate is linear.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnamb/302.html}
}
TY - JOUR
T1 - Monotone Iterates with Quadratic Convergence Rate for Solving Semilinear Parabolic Problems.
AU - Igor Boglaev
JO - International Journal of Numerical Analysis Modeling Series B
VL - 2
SP - 109
EP - 123
PY - 2011
DA - 2011/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/302.html
KW -
AB - This paper deals with numerical solving semilinear parabolic problems based on the
method of upper and lower solutions. A monotone iterative method with quadratic convergence
rate is constructed. The monotone iterative method combines an explicit construction of initial
upper and lower solutions and the modified accelerated monotone iterative method. The monotone
iterative method leads to the existence-uniqueness theorem. An analysis of convergence rates of
the monotone iterative method, based on different stoping tests, is given. Results of numerical
experiments are presented, where iteration counts are compared with a monotone iterative method,
whose convergence rate is linear.
Igor Boglaev. (2011). Monotone Iterates with Quadratic Convergence Rate for Solving Semilinear Parabolic Problems..
International Journal of Numerical Analysis Modeling Series B. 2 (2).
109-123.
doi:
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