Time dependent parameters in ode

Let’s say an non-linear first order ode...> dy_dt= c1-c2*e^y+1

• define t_span as t= 1:10 and initial value is 0.1
• c1=[1 1 2 2 3 4 4 3 1 0] and c2=[1 1 2 2 3 4 4 3 1 1]
• c1 & c2 is also vector of 1*10
• For every change in value of t from t_i-1 to t_i, c1 and c2 values should be updated in ode and final value of iteration t_i-1 should be initial value to t_i .Please suggest me how to proceed

[John D'Errico]

So are you telling us that c1 and c2 are actually functions of t? You will need to interpolate them, since the solver will usually need intermediate (non-integer) values of t.

[PUJARI MURAGA]

Yes.exactly, at time t1, c1(1) and c2(1) should be updated with ic y0 and at time t2, c1(2) c2(2) should be updated with ic as y1......and so on

[John D'Errico]

So use a spline. WTP? Or use interp1.

In your objective function, you know the value of t.

c1spl = spline(1:100,c1);

Pass it in and use it.

Answer 1

[rotton]

Here is MathWorks official answer, and the corresponding paragraph from ode45 documentation.

Note that interp1 does linear interpolation by default, so you might need to change that.