Why is the convolution so different from the analytical answer?

I am trying to graph the convolution of two functions.

t = linspace(0,5,1001);

xt = (exp(-t) + exp(-3*t)).*heaviside(t);

ht = (1.5.*exp(-2.*t) + 1.5.*exp(-4.*t)).*heaviside(t);

yt_n = conv(xt,ht);

yt_a = (2.*exp(-1.*t)-2.*exp(-4.*t)).*heaviside(t)

When comparing yt_n and yt_a, the results are very different. Though, they should be the same since yt_a is just the analytically derived output response for x(t) and y(t), Why is this?

Answer 1

[Paul]

When approximating the continuous convolution with a discrete convoluton, the discrete convolution needs to be multilplied by dt, which in this case is 0.005

plot(t,yt_a,t,yt_n(1:numel(t))*.005,'o'),grid

[Bradlee Harrison]

Thank you so much!