Geodesic
Method of interpolation for a~boundary layer problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 3, pp. 267-275

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A singularly perturbed boundary value problem for a second order ordinary differential equation is considered. It is assumed that the solution is found at the nodes of a uniform or nonuniform mesh. An interpolation method taking into account the boundary layer part of the solution is proposed. Using the constructed interpolation function, we find the derivative of the solution with an accuracy uniform with respect to a parameter at any point of the interval. 
@article{SJVM_2007_10_3_a3,
     author = {A. I. Zadorin},
     title = {Method of interpolation for a~boundary layer problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {267--275},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a3/}
}
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A. I. Zadorin. Method of interpolation for a~boundary layer problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 3, pp. 267-275. http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a3/