Geodesic
Numerical solution of a quasilinear parabolic equation with a boundary layer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 716-726 Cet article a éte moissonné depuis la source Math-Net.Ru

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To solve a quasilinear parabolic equation with small parameter multiplying the derivatives with respect to the spatial variables, a numerical method is constructed with an estimate of the error, which is uniform with respect to the parameter. The construction of a nonlinear difference scheme is based on the method of straight lines and on the application of exact systems to one-dimensional problems. The computational mesh is chosen so that its density increases in a suitable way in the neighbourhood of the boundary. We propose that the nonlinear scheme be solved by an iterative algorithm, which converges uniformly with respect to the small parameter. 
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I. P. Boglaev. Numerical solution of a quasilinear parabolic equation with a boundary layer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 716-726. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a7/

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