A higher-order scheme for quasilinear boundary value problems with two small parameters

Authors:
Relja Vulanović
Affiliations:
Kent State Univ., Canton, OH
Venue:
Computing
Year:
2001

Citing 7
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Abstract

A class of singularly perturbed quasilinear boundary value problems with two small parameters is solved numerically by finite differences on a Shishkin-type mesh. The discretization combines a four-point third-order scheme inside the boundary layers with the standard central scheme outside the layers. This results in an almost third-order accuracy which is uniform with respect to the perturbation parameters. The paper also shows that the Shishkin meshes are more suitable for higher-order schemes than the Bakhvalov meshes, since complicated nonequidistant schemes can be avoided.