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Volume 2, Issue 4
Monotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems.

IGOR BOGLAEV

Int. J. Numer. Anal. Mod. B, 2 (2011), pp. 402-414

Published online: 2011-02

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  • Abstract
This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-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.
  • Keywords

semilinear elliptic problem monotone difference schemes monotone relaxation iterates singularly perturbed problems uniform convergence

  • AMS Subject Headings

65H10 65F10 65N06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-2-402, author = {IGOR BOGLAEV}, title = {Monotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems. }, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2011}, volume = {2}, number = {4}, pages = {402--414}, abstract = {This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/320.html} }
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 ω-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.
IGOR BOGLAEV. (2011). Monotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems. . International Journal of Numerical Analysis Modeling Series B. 2 (4). 402-414. doi:
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