clear
L = 2; 
w = .3; 
d = .03; 
n = 1280; 
g = 9.81; %downward force due to gravity
h = L/n; %define variables
x = h:h:L;
I = w*d^3/12;
E = 1.3e10;
    
A = sparse(n,n); %initialize the matrix A
A(1,1:4) = [16 -9 8/3 -1/4]; %enter the fixed values for the matrix
A(2,1:4) = [-4 6 -4 1];
A(n-1,n-3:n) = [16/17 -60/17 72/17 -28/17];
A(n,n-3:n) = [-12/17 96/17 -156/17 72/17];
    
for i = 3:n-2 %use for loops to fill in the remaining entries in matrix A
    for j = 1:n
        A(i,i-2) = 1;
        A(i,i-1) = -4;
        A(i,i) = 6;
        A(i,i+1) = -4;
        A(i,i+2) = 1;
    end
end
        
f = -480*w*d*g;
fvector = f*ones(n,1);
index = n;
    
while h*index >= 1.8
    fvector(index) = fvector(index) - g*350;
    index = index - 1;
end
    
RHS = h^4/(E*I)*(fvector);
y = zeros(n,1);
ysolution = A\RHS;

figure();
plot(x,ysolution,'-',x,ysolution);
title('Computed Solution');
xlabel('x');
ylabel('y(x)');

ysolution(n)