Stop ode solver when a variable reach some value?

Hello, I have a diferential model of 12 equations, (I write down 3 of them) but I whant that ode solver stop when a variable reach 90% of its final value.

dR/dt = -k1*R*E+k_1*RE-p1u*CD*R+pd1u*Rp-k3*E7*R+k_3*RV;

dRp/dt = p1u*CD*R-p2u*CE*Rp-k2*Rp*E+k_2*RpE-pd1u*Rp+pd2u*Rpp-k4*E7*Rp+k_4*RpV;

dE/dt = -k1*R*E+k_1*RE-k2*Rp*E+k_2*RpE+p2c*CE*RpE+pi2c*CE*RpEV+k_8*RpEV+k_7*REV;

I need to stop ode solver when E gets 90% of its final value, I don't know If some body know D:.

Answer 1

[Davide Masiello]

You can use the MatLab ODE event location.

https://it.mathworks.com/help/matlab/math/ode-event-location.html

I will give an example below, but I will have to make up names since you gave too few info.

Let's assume your ODE function is called 'myfunc' and that E is the third variable

function out = myfunc(t,y)
R = y(1);
Rp = y(2);
E = y(3);
etc.

dR/dt = -k1*R*E+k_1*RE-p1u*CD*R+pd1u*Rp-k3*E7*R+k_3*RV;
dRp/dt = p1u*CD*R-p2u*CE*Rp-k2*Rp*E+k_2*RpE-pd1u*Rp+pd2u*Rpp-k4*E7*Rp+k_4*RpV;
dE/dt =   -k1*R*E+k_1*RE-k2*Rp*E+k_2*RpE+p2c*CE*RpE+pi2c*CE*RpEV+k_8*RpEV+k_7*REV;
etc.

out = [ dR/dt;...
        dRp/dt;...
        dE/dt;...
        etc.
        ]
end

if Ef is the final value of E, your ODE event locator function should look something like this.

function [position,isterminal,direction] = eventFcn(t,y,Ef)
position = y(3)-0.9*Ef; % The value that we want to be zero
isterminal = 1;  % Halt integration 
direction = 0;   % The zero can be approached from either direction
end

You can pass this function to the ODE options structure, which is then pass to the ODE solver

opts = odeset('Events',@(t,y)eventFcn(t,y,Ef));
[t,y] = ode45(@myfunc,tspan,y0,opts);

This should do it for you.

[Silvia Casillas]

Thank you for the answer, I actually was made something like that but my main problem whas to find Ef, Its suppose that I have to calcute first before I can made the event function right?

Again, tank you a lot fot help me.

[Davide Masiello]

Yes, you do need to know what the final value is if you want to stop the integration at 90% of that value, I don't see any way around that XD.