21
Piecewise Interpolation Polynomials
Abstract
Topics of this chapter are piecewise polynomial interpolations based on
Lagrange, Hermite, or extended Hermite polynomials of arbitrary degree. The
basic idea is to divide the space of interest into smaller subintervals carrying a
local coordinate system. Piecewise interpolation polynomials can be used, e.g.,
for interpolating data. The focus here are finite element applications in quantum
dynamics. Thus as an example we will apply piecewise Lagrange interpolation
polynomials for a finite element ansatz of the radial Schrödinger equation for
Hydrogen atoms. MATLAB code for computing the interpolation coefficients
and code with respect of the finite element example can be downloaded.
Topics of this chapter are piecewise polynomial interpolations based on Lagrange,
Hermite, or extended Hermite polynomials. The basic idea is to divide the space
of interest [x a , x b ] into smaller subintervals carrying a local coordinate system
˜
x running from [0, +1]. MATLAB offers many functions for interpolating data.
The intention here is to use piecewise interpolation polynomials, e.g., for solving
differential equations via finite elements. As an example we will apply interpolation
polynomials onto a finite element ansatz for the radial Schrödinger equation of the
Hydrogen atom.
Function Overview
The MATLAB-function pchip is a piecewise cubic Hermite interpolation polynomial, thus based on two nodal points. The SPECFUNPHYS-class ippolynom
returns the interpolation coefficients of arbitrary Lagrange, Hermite, or extended
Hermite polynomials and the function Hatomeig shows as an application the
finite element solution for the Hydrogen atom based on Lagrange interpolation
polynomials.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_21
237
Piecewise Interpolation Polynomials
Abstract
Topics of this chapter are piecewise polynomial interpolations based on
Lagrange, Hermite, or extended Hermite polynomials of arbitrary degree. The
basic idea is to divide the space of interest into smaller subintervals carrying a
local coordinate system. Piecewise interpolation polynomials can be used, e.g.,
for interpolating data. The focus here are finite element applications in quantum
dynamics. Thus as an example we will apply piecewise Lagrange interpolation
polynomials for a finite element ansatz of the radial Schrödinger equation for
Hydrogen atoms. MATLAB code for computing the interpolation coefficients
and code with respect of the finite element example can be downloaded.
Topics of this chapter are piecewise polynomial interpolations based on Lagrange,
Hermite, or extended Hermite polynomials. The basic idea is to divide the space
of interest [x a , x b ] into smaller subintervals carrying a local coordinate system
˜
x running from [0, +1]. MATLAB offers many functions for interpolating data.
The intention here is to use piecewise interpolation polynomials, e.g., for solving
differential equations via finite elements. As an example we will apply interpolation
polynomials onto a finite element ansatz for the radial Schrödinger equation of the
Hydrogen atom.
Function Overview
The MATLAB-function pchip is a piecewise cubic Hermite interpolation polynomial, thus based on two nodal points. The SPECFUNPHYS-class ippolynom
returns the interpolation coefficients of arbitrary Lagrange, Hermite, or extended
Hermite polynomials and the function Hatomeig shows as an application the
finite element solution for the Hydrogen atom based on Lagrange interpolation
polynomials.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_21
237