Bary: The Barycentric Interpolation in MatLab

Purpose

• The library "Bary" provides MatLab functions for the barycentric interpolation.

Click Here to Download the Codes


Specifications

• Name:Bary
• Author: Feng Chen
• Version: 1.0
• Language: MATLAB

Simple Example

• Equation: $$\begin{equation} \begin{aligned} &c_1(x)u''(x)+ c_2(x)u'(x)+c_3(x)u(x) = f(x), \quad \Omega = (a,b),\\ &u \text{ satisifies the general boundary condition}. \end{aligned} \end{equation}$$
• Parameters: $$\begin{equation} c_1(x)=-4x^2, \quad c_2(x) = 3x, \quad c_3(x)=2. \end{equation}$$
• Exact solution and input functions: $$\begin{equation} u(x) = \sin x , \end{equation}$$ then $f(x)$ is calculated accordingly.

Quick Start

• Compiling and running:

  matlab test_bvp
  

• Output:

   
  error =
  
     1.1180e-13
  

• CPU: Intel(R) Core(TM) i5-4590S CPU @ 3.00GHz
• OS: Ubuntu 18.04.
• Release: MATLAB R2019a.

References

• Tee, T. & Trefethen, L. A Rational Spectral Collocation Method with Adaptively Transformed Chebyshev Grid Points, SIAM Journal on Scientific Computing, Volume 28, Number 5, 1798-1811, (2006).

Core Subroutines

function [P L U A] = bc_bvp_matrix(c1, c2, c3, a1, a2, b1, b2, D1, D2)

n = length(c1);
A = diag(c1)*D2 + diag(c2)*D1 + diag(c3);
A(1,:) = a1*[1 zeros(1,n-1)] + b1*D1(1,:);
A(n,:) = a2*[zeros(1,n-1) 1] + b2*D1(n,:);
[L,U,P] = lu(A);