Convergence analysis of nite-diierence approximations of an inhomogeneous singularly perturbed boundary value problem using grid equidistribution. We derive-uniform error estimates for two rst-order upwind discretisations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, is the small parameter multiplying the highest derivative term...

A singularly perturbed boundary-value problem with a multiple turning point at a boundary is considered. A representation of the solution is given, and it is used in the construction of a uniform finite-difference scheme. The scheme is a fiNJt-order exponentially fitted one. An improved modification on a special discretization mesh is given.

A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.

For a singularly-perturbed two-point boundary value problem, we propose an ε-uniform finite difference method on an equidistant mesh which requires no exact solution of a differential equation. We start with a full-fitted operator method reflecting the singular perturbation nature of the problem through a local boundary value problem. However, to solve the local boundary value problem, we emplo...

In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the...

In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. Finally, an example is presented to show the result. 2000 Mathematics S...

Kolmogorov N-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the N-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

This paper is concerned with the upwind finite-difference discretization of a quasilinear singularly perturbed boundary value problem without turning points. Kopteva’s a posteriori error estimate [N. Kopteva, Maximum norm a posteriori error estimates for a onedimensional convection-diffusion problem, SIAM J. Numer. Anal., 39, 423–441 (2001)] is generalized and improved. 2000 MSC: 65L10, 65L70.