A higher-order scheme for quasilinear boundary value problems with two small parameters
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.
boundary value problem finite differences shishkin mesh singular perturbation uniform convergence