This paper focuses on the boundary layer phenomenon arising in the study of singularly perturbed differential equations. Our tools include the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear equations under consideration. Key words and phrases: singularly perturbed systems, three–point boundary value problem, method of l...

A numerical method based on cubic spline with exponential fitting factor is given for the selfadjoint singularly perturbed two-point boundary value problems. The scheme derived in this method is second-order accurate. Numerical examples are given to support the predicted theory.

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.

We consider singularly perturbed reaction-diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x, t, ε) with boundary layers and derive conditions for their asymptotic stability The boundary layer part of u(x, t, ε) is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary co...