Local piecewise polynomial curve of variable order and its appliance for calculating of nodal derivatives

TL;DR

This paper introduces a new Hermite-type piecewise polynomial curve of variable order with C1 continuity on nonuniform grids, providing methods for derivative calculation and demonstrating its properties through numerical experiments.

Contribution

The paper develops a novel Hermite-type piecewise polynomial curve adaptable to uniform and nonuniform grids, with derivative calculation methods and empirical validation.

Findings

The curve achieves C1 continuity on nonuniform grids.

Methods for calculating derivatives at knots are proposed.

Numerical experiments confirm the curve's desirable properties.

Abstract

In this paper, we present a new Hermite type curve piecewise polynomial of C1 continuity on nonuniform grids. Depending on the location of the knots of the grid (uniform and nonuniform), the curve is quadratic or cubic. The approximation error is investigated. For nonuniform grids a method for calculating the first and second derivatives in knots is proposed. We also perform several numerical experiments which exemplify the properties of the proposed curve. Graphic examples are given.