
For the problem: −Ɛy ′′(x)+p(x)y(x) = f(x); x ∈ D; y(0) = α 0; y(1) = α 1the spline difference schemes on a piecewise mesh having the second order of uniform convergence are given. Also, in this paper is presented a construction of an uniformly convergent scheme with an almost fourth order of uniform convergence on a Shishkin mesh.
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