Automatically return derivative from ode solver at each solution point in Matlab?

Question

The standard Matlab ode45 call is:

[T,Y] = solver(odefun,tspan,y0,options);

But I also want the value of odefunat each state vector Y. It seems like there should be an option to return something like

[T,Y, DYDT] = solver(odefun,tspan,y0,options);

as this would be the most efficient way, since the routine already evaluates the derivative at each point internally. The obvious work around is to do

DYDT = odefun(T,Y);

however then I would need to write a modified version of odefun since the one you pass to the solver should be a column vector denoting a single state. Here obviously I am wanting to calculate DYDT at all states Y returned by the solver. Any suggestions?

Sergio Haram Sergio Haram · Accepted Answer · 2014-10-10T11:42:27

I don't believe there is away to get the derivative directly.

May be you could try something like:

tspan = 0:0.001:5; % choose a time-interval
x0 = 5 % and an initial condition

run you ode45 code

[~,xt_solution]=ode45('odefun',tspan,x0);

and then diffenrentiate your solution:

tdiff=diff(tspan);
xdiff=diff(xt_solution);
dxdt=xdiff1./tdiff1;

And there you go. You will have the values of the derivative together with its corresponding tspan value! Just remember that your ´dxdt´ array will have one element less than xt_solution. This is because of the way we are differentiating xt_solution

If you must have both arrays of the same dim you can go:

if size(xt_solution,1) > size(dxdt,1)
    xt_solution = xt_solution(1:size(dxdt,1),:);
end

So the trick is to predefine your tspan from before and then use it to find the derivative!

Automatically return derivative from ode solver at each solution point in Matlab?

2 Answers