Two upwind finite difference schemes are considered for the numerical solution of a class of semilinear convection-diffusion problems with a small perturbation parameter ε and an attractive boundary turning point. We show that for both schemes the maximum nodal error is bounded by a special weighted `1-type norm of the truncation error. These results are used to establish ε-uniform pointwise co...

aims: the installation of intravenous catheter is an unpleasant and painful experience for many patients. then, it is necessary to provide new methods to either reduce or remove pain in the patients’ injection point. the aim of this study was to investigate the effects of positioning (either sitting or lying) during the installation of intravenous catheter on pain level and the following anxiet...

We study interpolation of a function two variables with large gradients in regions boundary layer under the assumption that Shishkin decomposition into sum regular and components is valid for interpolated function. generalize one-dimensional cubic splines, studied earlier on Bakhvalov grids, to two-dimensional case. obtain error estimates spline interpolation, uniform small parameter.

Pointwise accurate numerical methods are constructed and analysed for three classes of singularly perturbed first order transport problems. The involve piecewise-uniform Shishkin meshes the approximations shown to be parameter-uniformly convergent in maximum norm. A problem from modelling fluid–particle interaction is formulated used as a test these methods. Numerical results presented illustra...

A numerical algorithm is presented to solve a benchmark problem proposed by Hemker (1996). The incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due geometries and associated layer structures that involved in this problem. Numerical results demonstrate effectiveness algorithm.

In this paper, we consider the local discontinuous Galerkin method (LDG) for solving singularly perturbed convection-diffusion problems in oneand two-dimensional settings. The existence and uniqueness of the LDG solutions are verified. Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes. Thanks to the implementa...