Volume 2, Issue 2
Semi-Linear Difference Schemes
DOI:

J. Comp. Math., 2 (1984), pp. 93-111

Published online: 1984-02

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• Abstract

A class of smi-linear numerical differentiation formulas is designed for functions with steep gradients. A semi-linear second-order difference scheme is constructed to solve the two-point singular perturbation problem. It is shown that this semi-linear scheme has one more order of approximation precision than the central difference scheme for small $\epsilon$ and saves computation time for required accuracy. Numerical results agreeing with the above analysis are included.

• Keywords

@Article{JCM-2-93, author = {Jia-Chang Sun}, title = {Semi-Linear Difference Schemes}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {2}, pages = {93--111}, abstract = { A class of smi-linear numerical differentiation formulas is designed for functions with steep gradients. A semi-linear second-order difference scheme is constructed to solve the two-point singular perturbation problem. It is shown that this semi-linear scheme has one more order of approximation precision than the central difference scheme for small $\epsilon$ and saves computation time for required accuracy. Numerical results agreeing with the above analysis are included. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9644.html} }
TY - JOUR T1 - Semi-Linear Difference Schemes AU - Jia-Chang Sun JO - Journal of Computational Mathematics VL - 2 SP - 93 EP - 111 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9644.html KW - AB - A class of smi-linear numerical differentiation formulas is designed for functions with steep gradients. A semi-linear second-order difference scheme is constructed to solve the two-point singular perturbation problem. It is shown that this semi-linear scheme has one more order of approximation precision than the central difference scheme for small $\epsilon$ and saves computation time for required accuracy. Numerical results agreeing with the above analysis are included.