One-dimensional mesh generation for critical points in an interval

Abstract

We provide a general theory for the generation of one-dimensional non-uniform meshes. From this theory, we derive simple procedures for the calculation of meshes wherein the density of points are concentrated in the neighborhood of a critical point, namely, a Lorentzian- and an exponential-type mesh. The latter is especially useful when the critical point is on one of the ex-tremes of the interval. Examples are provided in order to show that the considered non-uniform meshes improve the interpolation with respect to a uniform mesh.