Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods - Dialla Konate (International Journal of Mathematics and Mathematical Sciences)
It is well known that a polynomial-based approximation scheme applied to a singularly perturbed equation is not uniformly convergent over the geometric domain of study. Such scheme results in a numerical solution, say σ which suffers from severe inaccuracies particularly in the boundary layer. What we say in the current paper is this: when one uses a grid which is not too coarse the resulted solution, even being nonuniformly convergent may be used in an iterated scheme to get a good approximation solution that is uniformly convergent over the whole geometric domain of study.