TY - JOUR T1 - Semi-Linear Difference Schemes 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 semi-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.