Semi-Linear Difference Schemes (Journal of Computational Mathematics, 1984)
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 $ε$ and saves computation time for required accuracy. Numerical results agreeing with the above analysis are included.