A stable high-order interpolation scheme for superconvergent data

A local collocation scheme is developed that yields stable high-order accurate interpolants of discrete data arising from the numerical solution of a differential equation. It should prove to be especially attractive for applications where data are superconvergent, e.g., spline collocation at Gauss points. For simplicity, the formulas are initially developed for a scalar equation, but generalizations are later given for systems. Numerical examples are shown that illustrate the stability, even for the case of highly nonuniform meshes which have proven difficult in prior studies.