This paper deals with uniform convergent methods for solving singularly perturbed two-point boundary value problems with piecewise smooth coefficients. Construction of the numerical methods is based on locally exact schemes or on local Green’s functions. Uniform convergent properties of the proposed methods on arbitrary meshes are proven. Numerical experiments are presented.

A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation p...

Abstract. A class of methods constructed to numerically approximate the solution of two-point singularly perturbed boundary value problems of the form εu + bu + cu = f use exponentials to mimic exponential behavior of the solution in the boundary layer(s). We refer to them as exponentially fitted methods. Such methods are usually exact on polynomials of certain degree and some exponential funct...

A numerical method based on parametric spline with adaptive parameter is given for the secondorder singularly perturbed two-point boundary value problems of the form 0 1 ( ) ( ) ( ); ( ) ; ( ) y p x y q x y r x y a y b           The derived method is second-order and fourth-order convergence depending on the choice of the two parameters  and  . Error analysis of a method is briefly...

Abstract In this paper a fitted second-order finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at both end (left and right) points. We have introduced a fitting factor in second-order tri-diagonal finite difference scheme and it is obtained from the theory of singular perturbations. The efficient Thomas algorithm is ...

We consider the numerical approximation of singularly perturbed elliptic boundary value problems over non-smooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield nite element spaces with robust approximation properties. In particular, we const...