MATLAB: Adding a piecewise time dependent term in system of differential equation

differential equationsif statementMATLAB

Problem Statement: I have a system of differential equation and out of which few has time dependent coefficients and in my case i have piecewise time dependence. I am unable to add the time dependence and solve the equation.
Simplified Differential Equation:
My time span runs from 0 to 360 days and my aim is to have certain nonzero value for for half a day and zero for other half.
My unsuccessful attempt:
Function definition: MWE_fn.m
function rk1 = MWE_fn(t,y)
r2=0.5;b2=1;d_A=0.05; c=0.5;
rk1(1)=r2*y(1)*(1-b2*y(1))-c*y(1)*y(2);
rk1(2)= A0(t)- d_A*y(2);
rk1=rk1(:);
end
function fa=A0(t)
    if rem(t,1)==0
        fa=0.04
    else 
        fa=0
    end
end
Function Body: MWE_body.m
timerange= 0:0.5:360;
IC= [0.1,0];%initial conditions 
[t,y] =ode45(@(t,y) MWE_fn(t,y),timerange, IC);
plot(t,y(:,1),'b');
hold on
plot(t,y(:,2),'r');
I was aiming to write some kind of conditional statement for the function to take those values but that didn't go correct. The thing i had in mind was that for half a day we have time at integer values and for other half i have time at 0.5 , so i used a rem function to check that, but i was wrong and it didn't work.
Anyhelp would be appreciated.
Thank You.

Best Answer

The conditional statement idea is right, the problem was that you considered that the ode45 would evaluate your function only at the time steps you gave, which is not right. To perform the integration many other time intervals are needed, so you just have to adjust your conditional:
function fa=A0(t)
    if t>round(t)
        fa=0.04;
    else 
        fa=0;
    end
    
end
In this case, for every value x.y where y<5, fa = 0.04, which represents basically all your half days
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