solving system of equations

Hi, I have the following three equations:

a = Q/k*(N1+ N2);

b = Q/k*(N1 + N2);

dQ/dt = r - k*(N1*a + N2*b);

where, r, k, N1, and N2 are parameters. I am a newbie to Matlab. I know I should use ode45 to solve for Q and provide an initial value. But, I could not quite figure out how to use values of Q to calculate a and b. Can anyone please help? Thank you. -Sam

Answer 1

[James Tursa]

1) Look at the examples here:

https://www.mathworks.com/help/matlab/ref/ode45.html?searchHighlight=ode45&s_tid=doc_srchtitle

2) Write your derivative function. E.g., it will look something like this:

function dQdt = Qdot(t,Q,r,k,N1,N2)
a = etc     <-- you fill in the rhs
b = etc     <-- you fill in the rhs
dQdt = etc  <-- you fill in the rhs
end

3) You write code to call ode45. E.g., an outline

r = etc
k = etc
N1 = etc
N2 = etc
Q0 = etc  <-- the initial condition
tspan = etc  <-- the time span
[t,Q] = ode45(@(t,Q) Qdot(t,Q,r,k,N1,N2), tspan, Q0);

Then plot the results, or whatever the assignment calls for.

[Sam K]

Thank you James. That worked for me. I have a quick follow-up question. I figured out how to plot Q. But, I need to plot a and b as well. How can I do that? Thank you.

[James Tursa]

Since a and b are functions of everything you have in your workspace, simply calculate them directly after you call ode45:

a = Q/k*(N1 + N2);
b = Q/k*(N1 + N2);