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Volume 5, Issue 1
A Uniformly Convergent Method on Arbitrary Meshes for a Semilinear Convection-Diffusion Problem with Discontinuous Data

Igor Boglaev & Sophie Pack

Int. J. Numer. Anal. Mod., 5 (2008), pp. 24-39.

Published online: 2008-05

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  • Abstract

This paper deals with a uniform (in a perturbation parameter) convergent difference scheme for solving a nonlinear singularly perturbed two-point boundary value problem with discontinuous data of a convection-diffusion type. Construction of the difference scheme is based on locally exact schemes or on local Green's functions. Uniform convergence with first order of the proposed difference scheme on arbitrary meshes is proven. A monotone iterative method, which is based on the method of upper and lower solutions, is applied to computing the nonlinear difference scheme. Numerical experiments are presented.

  • Keywords

convection-diffusion problem, discontinuous data, boundary layer, uniform convergence, monotone iterative method.

  • AMS Subject Headings

65L10, 65L20, 65L70, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-24, author = {Boglaev , Igor and Pack , Sophie}, title = {A Uniformly Convergent Method on Arbitrary Meshes for a Semilinear Convection-Diffusion Problem with Discontinuous Data}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {1}, pages = {24--39}, abstract = {

This paper deals with a uniform (in a perturbation parameter) convergent difference scheme for solving a nonlinear singularly perturbed two-point boundary value problem with discontinuous data of a convection-diffusion type. Construction of the difference scheme is based on locally exact schemes or on local Green's functions. Uniform convergence with first order of the proposed difference scheme on arbitrary meshes is proven. A monotone iterative method, which is based on the method of upper and lower solutions, is applied to computing the nonlinear difference scheme. Numerical experiments are presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/795.html} }
TY - JOUR T1 - A Uniformly Convergent Method on Arbitrary Meshes for a Semilinear Convection-Diffusion Problem with Discontinuous Data AU - Boglaev , Igor AU - Pack , Sophie JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 24 EP - 39 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/795.html KW - convection-diffusion problem, discontinuous data, boundary layer, uniform convergence, monotone iterative method. AB -

This paper deals with a uniform (in a perturbation parameter) convergent difference scheme for solving a nonlinear singularly perturbed two-point boundary value problem with discontinuous data of a convection-diffusion type. Construction of the difference scheme is based on locally exact schemes or on local Green's functions. Uniform convergence with first order of the proposed difference scheme on arbitrary meshes is proven. A monotone iterative method, which is based on the method of upper and lower solutions, is applied to computing the nonlinear difference scheme. Numerical experiments are presented.

Boglaev , Igor and Pack , Sophie. (2008). A Uniformly Convergent Method on Arbitrary Meshes for a Semilinear Convection-Diffusion Problem with Discontinuous Data. International Journal of Numerical Analysis and Modeling. 5 (1). 24-39. doi:
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