Time-dependent parameter in ODE solver

I was trying to understand how to deal with time-dependent parameter in ODE solver. Having this error "Error using interp1>reshapeAndSortXandV - X and V must be of the same length."

Please explain what the issue.

tspan = 1:5;
y0 = 0;
a = 1:5;
[t,y] = ode45(@(t,y)fun(t,y,a),tspan, y0);

function v = fun(t,y,a)
t_dummy = t;
a = interp1(t_dummy,a,t);
v = 2*a.*t;
end

Answer 1

[Star Strider]

The interp1 use in the documentation section for time-dependent parameters refers to vector arguments with a dependent variable as a function of time. The interpolation would then return an interpolated value of the dependent variable at a specific time.

You need to pass ‘tv’ (or some other time vector with appropriate limits) to ‘fun’ as well in order to do the interpolation —

tspan = 1:5;
y0 = 0;
a = 1:5;
tv = 1:5;
[t,y] = ode45(@(t,y)fun(t,y,a,tv),tspan, y0);

figure
plot(t, y)
grid
xlabel('Time')
ylabel('Y')

function v = fun(t,y,a,tv)
a = interp1(tv,a,t);
v = 2*a.*t;
end

That produces a consistent result.

.

[Monirul Hasan]

Got it. Thanks you.

[Star Strider]

As always, my pleasure!