central_diff20.m

function B = central_diff20(q) 
%This function of q uses central difference approximation to set up a system of
%equations while using numerical differentiation to determine the value of the end points. 
x=1/20; %splits up beam into twenty
b=0.1; %width of beam
E=70E9; %Young's modulus 
h=0.01;%height of beam 
I=(b*(h^3))/12; %Second MOI
z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement

Seg20= [5,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
   -4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
   1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
   0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0;
   0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0;
   0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0;
   0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0;
   0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0;
   0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0;
   0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0;
   0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0;
   0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0;
   0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0;
   0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0;
   0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0;
   0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0;
   0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1;
   0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4;
   0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,5];

Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];
B=Seg20\Y;