Abstract
A boundary value problem for a second-order nonlinear singular perturbation ordinary differential equation is considered. A method based on Newton and Picard linearizations using a modified Samarskii scheme on a Shishkin grid for a linear problem is proposed. It is proved that the difference schemes are of second-order and uniformly convergent. To decrease the number of arithmetic operations, a two-grid method is proposed. The results of some numerical experiments are discussed.
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