Geodesic
A First Order Accuracy Scheme on Non-uniform Mesh
Publications de l'Institut Mathématique, _N_S_42 (1987) no. 56, p. 155

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

It is proved that the exponentially fitted quadratic spline difference scheme derived in [5] and applied to the singularly perturbed two-point boundary value problem $ \aligned \varepsilon y''+p(x)y'=f(x),\quad 00. \endaligned $ has the first order of uniform convergence on non-uniform mesh. In order to achieve the uniform first order accuracy the special "almost uniform mesh" which satisfies the condition $h_i=h_{i-1}+Mh_{i-1}\max(x_i,\varepsilon)$ was constructed. The results are illustrated by numerical experiments. 
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     author = {Mirjana Stojanovi\'c},
     title = {A {First} {Order} {Accuracy} {Scheme} on {Non-uniform} {Mesh}},
     journal = {Publications de l'Institut Math\'ematique},
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     publisher = {mathdoc},
     volume = {_N_S_42},
     number = {56},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1987_N_S_42_56_a17/}
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Mirjana Stojanović. A First Order Accuracy Scheme on Non-uniform Mesh. Publications de l'Institut Mathématique, _N_S_42 (1987) no. 56, p. 155 . http://geodesic.mathdoc.fr/item/PIM_1987_N_S_42_56_a17/