Geodesic
Numerical solution of an equation with a small parameter multiplying the highest derivative
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 620-628

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A family of monotonic difference schemes on a non-uniform mesh is proposed for solving a second-order ordinary differential equation with a small parameter in the highest derivative. It is shown that, under certain conditions on the coefficients of the equation, the difference scheme is ill-posed. Two methods are given for solving an ill-posed difference problem, which are stable to rounding errors. 
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     author = {A. I. Zadorin and V. N. Ignat'ev},
     title = {Numerical solution of an equation with a small parameter multiplying the highest derivative},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     volume = {23},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a10/}
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A. I. Zadorin; V. N. Ignat'ev. Numerical solution of an equation with a small parameter multiplying the highest derivative. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 620-628. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a10/