A Stable High-Order Interpolation Scheme for Superconvergent Data

@article{Pruess1996ASH,
  title={A Stable High-Order Interpolation Scheme for Superconvergent Data},
  author={Steven Pruess and Hong Sung Jin},
  journal={SIAM J. Scientific Computing},
  year={1996},
  volume={17},
  pages={714-724}
}
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… CONTINUE READING