Superconvergence points for higher-order derivative interpolation and its applications in spectral collocation method

In this work, we aim to investigate the superconvergence phenomenon observed in the interpolation of higher-order derivatives. Our primary focus is on identifying the specific points where the function values of the interpolant exhibit superconvergence, particularly when interpolating fourth- or fifth-order derivatives. These insights are then applied to refine the approximation of solutions for differential equations through well-conditioned spectral collocation methods. The numerical results demonstrate that the outputs obtained at these superconvergence points can achieve a higher level of accuracy. (c) 2024 Elsevier Inc. All rights reserved.