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Volume 7, Issue 3
A Uniform Numerical Method for a Boundary-Shock Problem

R. Vulanović

Int. J. Numer. Anal. Mod., 7 (2010), pp. 567-579.

Published online: 2010-07

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  • Abstract

A singularly perturbed quasilinear boundary-value problem is considered in the case when its solution has a boundary shock. The problem is discretized by an upwind finite-difference scheme on a mesh of Shishkin type. It is proved that this numerical method has pointwise accuracy of almost first order, which is uniform in the perturbation parameter.

  • Keywords

Boundary-value problem, singular perturbation, boundary shock, finite differences, Shishkin mesh, uniform convergence.

  • AMS Subject Headings

65L10, 65L12, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-567, author = {Vulanović , R.}, title = {A Uniform Numerical Method for a Boundary-Shock Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {567--579}, abstract = {

A singularly perturbed quasilinear boundary-value problem is considered in the case when its solution has a boundary shock. The problem is discretized by an upwind finite-difference scheme on a mesh of Shishkin type. It is proved that this numerical method has pointwise accuracy of almost first order, which is uniform in the perturbation parameter.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/738.html} }
TY - JOUR T1 - A Uniform Numerical Method for a Boundary-Shock Problem AU - Vulanović , R. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 567 EP - 579 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/738.html KW - Boundary-value problem, singular perturbation, boundary shock, finite differences, Shishkin mesh, uniform convergence. AB -

A singularly perturbed quasilinear boundary-value problem is considered in the case when its solution has a boundary shock. The problem is discretized by an upwind finite-difference scheme on a mesh of Shishkin type. It is proved that this numerical method has pointwise accuracy of almost first order, which is uniform in the perturbation parameter.

R. Vulanović. (1970). A Uniform Numerical Method for a Boundary-Shock Problem. International Journal of Numerical Analysis and Modeling. 7 (3). 567-579. doi:
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