Finite diierence schemes for singularly perturbed convection problems are studied in the limit case in which the viscosity approaches zero with the mesh-size. The error estimates allow choosing in advance appropriate schemes and mesh-resolutions for both boundary layer problems and circulating ow problems.

For a second-order quasilinear singularly perturbed problem under the Dirichlet boundary conditions, we propose new asymptotic numerical method, which involves two problems: reduced with one-side condition and novel layer correction two-sided condition. Through introduction of variables, both problems are transformed to set three first-order initial value zero conditions. The Runge–Kutta method...