A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition

Abstract

Based on the basis of B-spline functions an efficient numerical scheme on a piecewise-uniform mesh is suggested to approximate the solution of singularly perturbed problems with an integral boundary condition and having a delay of unit magnitude. For the small diffusion parameter $$\varepsilon $$, an interior layer and a boundary layer occur in the solution. Unlike most numerical schemes our scheme does not require the differentiation of the problem data (integral boundary condition). The parameter-uniform convergence (the second-order convergence except for a logarithmic factor) is confirmed by numerical computations of two test problems. As a variant double mesh principle is used to measure the accuracy of the method in terms of the maximum absolute error.