# -*- coding: utf-8 -*-
"""
Created on Wed Apr 28 12:53:20 2021

@author: neil
"""

# xi's are the nodal locations
# this code fills in the A matrix, and the C forcing vector, leaves top and bottom
# rows empty
for k in range(1,len(xi)-1):
    le0 = xi[k] - xi[k-1] # element lengths
    le1 = xi[k+1] - xi[k]
    A[k,k-1] = le0/6
    A[k,k]   = le0/3 + le1/3
    A[k,k+1] = le1/6
    C[k]     = (np.sin(xi[k])-np.sin(xi[k-1]))/le0 - (np.sin(xi[k+1])-np.sin(xi[k]))/le1