How to code a pulse function in differential equations

Hello everyone,

could you help me with my problem described below?

assuming I have a simple model dX/dt = -k*X/V, where X is amount, t is time (between 0 and 24 hours), V is volume, and k is rate.

I would like to add a certain amount of mass (M) into my system every 1 hour, in other words, adding mass on 1, 2, 3...23 hour. It does not need to be exactly on every hour, but could be a small interval (tau) around 1, 2, 3, ... so equation becomes something like

dX/dt = -k*X/V + M/tau, M is zero when t is out of these small intervals.

I just cannot figure out a smart way to code this, and then solve the ODE. Could you give me some idea? Thanks in advance!

Rui

[태훈]

If you can't get explicit solutions, I guess you could try "a series of odes" using a for loop. For example,...

tv=[0:1:100]

y0=1

for k=1:length(t)-1

tspan=[tv(k), tv(k+1)];

[t,y]=ode45(@yourfun, tspan...)

y0=y(length(y))+1 % e.g., adding 1 at every 1 hour

end