Geodesic
An almost fourth order uniformly convergent scheme for reaction-diffusion problems on a piecewise uniform grid
Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 51-59

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For the problem: $-\varepsilon y^{\prime\prime}(x) + p(x) y(x) = f(x),\;\: x \in D, \;\: y(0)=\alpha_{0},\, y(1)=\alpha_{1}$ the 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. 
@article{CHEB_2011_12_1_a3,
     author = {Vanja Vukoslav\v{c}evi\'c},
     title = {An almost fourth order uniformly convergent scheme for reaction-diffusion problems on a piecewise uniform grid},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {51--59},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a3/}
}
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Vanja Vukoslavčević. An almost fourth order uniformly convergent scheme for reaction-diffusion problems on a piecewise uniform grid. Čebyševskij sbornik, Tome 12 (2011) no. 1, pp. 51-59. http://geodesic.mathdoc.fr/item/CHEB_2011_12_1_a3/