Geodesic
A First Order Accuracy Scheme on Non-uniform Mesh
Publications de l'Institut Mathématique, _N_S_42 (1987) no. 56, p. 155
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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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     year = {1987},
     volume = {_N_S_42},
     number = {56},
     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/