Volume 8, Issue 1
A Completely Exponentially Fitted Difference Scheme for a Singular Perturbation Problem
DOI:

J. Comp. Math., 8 (1990), pp. 1-15

Published online: 1990-08

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• Abstract

A completely exponentially fitted difference scheme is considered for the singular perturbation problem:$\epsilon U^{''}+a(x) U^{'}-b(x) U=f(x) for 0 \lt x \lt 1$, with U(0), and U(1) given, $\epsilon \in (0,1]$ and a(x) \gt a \gt 0, b(x)$\geq 0$. It is proven that the scheme is uniformly second-order accurate.

• Keywords

@Article{JCM-8-1, author = {}, title = {A Completely Exponentially Fitted Difference Scheme for a Singular Perturbation Problem}, journal = {Journal of Computational Mathematics}, year = {1990}, volume = {8}, number = {1}, pages = {1--15}, abstract = { A completely exponentially fitted difference scheme is considered for the singular perturbation problem:$\epsilon U^{''}+a(x) U^{'}-b(x) U=f(x) for 0 \lt x \lt 1$, with U(0), and U(1) given, $\epsilon \in (0,1]$ and a(x) \gt a \gt 0, b(x)$\geq 0$. It is proven that the scheme is uniformly second-order accurate. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9414.html} }
TY - JOUR T1 - A Completely Exponentially Fitted Difference Scheme for a Singular Perturbation Problem JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 15 PY - 1990 DA - 1990/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9414.html KW - AB - A completely exponentially fitted difference scheme is considered for the singular perturbation problem:$\epsilon U^{''}+a(x) U^{'}-b(x) U=f(x) for 0 \lt x \lt 1$, with U(0), and U(1) given, $\epsilon \in (0,1]$ and a(x) \gt a \gt 0, b(x)$\geq 0$. It is proven that the scheme is uniformly second-order accurate.