n = 10;
L = 2;
w = .3;
d = .03;
h = L/n; %define variables
x = h:h:L;
I = w*d^3/12;
E = 1.3e10;
g = 9.81; %downward force due to gravity

A = zeros(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);
RHS = h^4/(E*I)*(fvector);
y = zeros(n,1);
ysolution = A\RHS;
yactual = ((f/(24*E*I)).*x.^2.*(x.^2-4*L.*x+6*L^2))';
error = abs(ysolution - yactual);
endpointerror = abs(ysolution(n) - yactual(n));

figure();
plot(x,ysolution,'ro',x,yactual);
title('Plot of Approximate Solution vs. Correct Solution');
xlabel('x');
ylabel('y(x)');

figure();
semilogy(x,error,2,endpointerror,'ro');axis([0 2 0 10e-16]);
title('Plot of Error');
xlabel('x');
ylabel('log(error)');