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Volume 9, Issue 4
On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters

Relja Vulanovic

J. Comp. Math., 9 (1991), pp. 321-329.

Published online: 1991-09

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  • Abstract

We consider the singular perturbation problem $$-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0,u(0),u(1)$$ given with two small parameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$. The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well.

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@Article{JCM-9-321, author = {Relja Vulanovic}, title = {On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {4}, pages = {321--329}, abstract = {

We consider the singular perturbation problem $$-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0,u(0),u(1)$$ given with two small parameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$. The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9407.html} }
TY - JOUR T1 - On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters AU - Relja Vulanovic JO - Journal of Computational Mathematics VL - 4 SP - 321 EP - 329 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9407.html KW - AB -

We consider the singular perturbation problem $$-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0,u(0),u(1)$$ given with two small parameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$. The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well.

Relja Vulanovic. (1991). On Numerical Solution of Quasilinear Boundary Value Problems with Two Small Parameters. Journal of Computational Mathematics. 9 (4). 321-329. doi:
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