% Runga Kutta
clear 
dt = 0.01;

t = 0:dt:100*pi;
s = size(t);

yt = 1;
vt = 0;
er2 = 0;

for i = 1:1:s(1,2)
    
    ky1 = dt*vt;
    kv1 = -dt*yt;
    
    ky2 = dt*(vt + ky1/2.0);
    kv2 = -dt*(yt + kv1/2.0);
    
    ky3 = dt*(vt + ky2/2.0);
    kv3 = -dt*(yt + kv2/2.0);
    
    ky4 = dt*(vt + ky3);
    kv4 = -dt*(yt + kv3);
    
    yt = yt +ky1/6.0 + ky2/3.0+ky3/3.0+ky4/6.0;
    vt = vt + kv1/6.0 + kv2/3.0 + kv3/3.0 + kv4/6.0;
    
    er2 = er2 + abs(cos(t(i))-yt);
    
end

er2 = er2/s(1,2)
er2fn = abs(cos(t(i))-yt)

slop2fn = vt