TY - JOUR T1 - A Uniform Numerical Method for a Boundary-Shock Problem AU - Vulanović , R. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 567 EP - 579 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/738.html KW - Boundary-value problem, singular perturbation, boundary shock, finite differences, Shishkin mesh, uniform convergence. AB -
A singularly perturbed quasilinear boundary-value problem is considered in the case when its solution has a boundary shock. The problem is discretized by an upwind finite-difference scheme on a mesh of Shishkin type. It is proved that this numerical method has pointwise accuracy of almost first order, which is uniform in the perturbation parameter.