Multiple outputs of Matlab ODE solver

Question

I have the following Matlab ODE code:

[t,y,~,~,ie] = ode23tb(@(t,y) RHSODE(t,y),[0,t_end], [i0;v0],options);

I want the ODE solver could also give me the result z, which is a function of y and dy/dt, such that z = f(y,dy/dt).

Does anyone know how to add such z into the output of the solver?

Answer 1

There are two ways to do this. The most common, and usually fastest, way is to take advantage of your integration function ( RHSODE in your case) and evaluate your function f after performing the integration. You haven't provided many details with your code but it might look something like this:

ydot = RHSODE(t,y);
z = f(y,ydot);

where t and y are the outputs from ode23tb . This requires that both RHSODE and f be vectorized (or you can wrap the above in a for loop).

The other way requires that you create an additional equation (or equations if z is a vector) inside of your integration function, RHSODE . Normally ode23tb integrates anything in this function so f must be multiplied by a factor of t to cancel this out. Again, your code might look something like this:

function ydot = RHSODE(t,y)
ydot0 = ... % Your original ODE(s)
z = f(y,ydot);
ydot = [ydot0;z*t]; % Make column vector