One-dimensional mesh generation for critical points in an interval
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 extremes 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.
Keywords: one-dimensional meshes, interpolation.