format compact
%Liður 1
n=10;
A = conv2(eye(n),[1,-4,6,-4,1],'same');
A(1,1)=16;
A(1,2)=-9;
A(1,3)=8/3;
A(1,4)=-1/4;
A(9,7)=16/17;
A(9,8)=-60/17;
A(9,9)=72/17;
A(9,10)=-28/17;
A(10,7)=-12/17;
A(10,8)=96/17;
A(10,9)=-156/17;
A(10,10)=72/17;
A=A;
f=-480*0.3*0.03*9.81;
f_v=f*ones(10,1);
h=0.2;
E=1.3e10;
I=0.3*0.03^3/12;
f_v=h^4/(E*I).*f_v;
y=A\f_v;

%Liður 2
L=2;
x=0.2:0.2:2;
y_x =(f/(24*E*I)).*x.^2.*(x.^2-4*L.*x+6*L^2);

plot(x,y_x)
hold on
plot(x,y,'o')
title('Graf 1')
xlabel('lengd [m]')
ylabel('hæð [m]')
% j=0.2;
% error=ones(n,1);
%     for i=1:10
%         y(i)-(f/(24*E*I)).*j.^2.*(j.^2-4*L.*j+6*L^2)
%         j=j+0.2;
%     end
error = y(n)-(f/(24*E*I)).*2.^2.*(2.^2-4*L.*2+6*L^2);

%Liður 3
for k = 1:6
       n=10*2^k;
%        nvalue(k)= n;
    A = sparse(n,n);
    A = conv2(eye(n),[1,-4,6,-4,1],'same');
    A(1,1)=16;
    A(1,2)=-9;
    A(1,3)=8/3;
    A(1,4)=-1/4;
    A(n-1,n-3)=16/17;
    A(n-1,n-2)=-60/17;
    A(n-1,n-1)=72/17;
    A(n-1,n)=-28/17;
    A(n,n-3)=-12/17;
    A(n,n-2)=96/17;
    A(n,n-1)=-156/17;
    A(n,n)=72/17;
    A=A;


%     condition(k) = cond(A);
%     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);
%     errors(k) = error(n)

    f=-480*0.3*0.03*9.81;
    f_v=f*ones(n,1);
    h=L/n;
    E=1.3e10;
    x=h:h:L;
    I=0.3*0.03^3/12;
    f_v=h^4/(E*I).*f_v;
    y = zeros(n,1);
    y=A\f_v;
    errors = y(n)-((f/(24*E*I))*L^2*(L^2-4*L*L+6*L^2))'
end