How to use Eventfunction for this ODE set?
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The main variables are R and N.
I want to switch between the functions externally or internally.
I know Event function can help but cannot implement it for this case.
EDIT : (working code based on Jan's template)
clc
clear
close all
y0 = [0,0,0,0]; %random initial nos.
t0 = 0; %random no.
tEnd = 10; %random no.
opt = odeset('RelTol', 1e-3);
y = y0;
t = t0;
State = 1;
while t(end) < tEnd
yprime = myFunction(t, y, State);
if yprime(2) > yprime(3)
State = 1;
disp('state is changed')
else
State = 2;
disp('state is changed')
end
fcn = @(t,y) myFunction(t, y, State);
opt = odeset('Events', @(t, y) myEvents(t,y,State));
[at, ay] = ode45(fcn, [t(end), tEnd], y(end, :),opt);
t = cat(1, t, at(2:end));
y = cat(1, y, ay(2:end, :));
end
%solution check
plot(t,y(:,4),'o') %plot results
hold on
z11 = 15*t.^2 - (40/3)*t.^3;
z22 = 50*t.^2 - 1000*t;
plot(t,z11,t, z22) %plot analytical results
figure(2)
z1 = 30*t - 40*t.^2;
z2 = 100*t - 1000;
plot(t,z1,t, z2) %plot ode set %note the intersection point
function [yprime] = myFunction(t, y, State)
yprime = [5*t; 30*t - 40*t.^2 ; 100*t - 1000 ]; %random funcs.
if State == 1
yprime(4) = yprime(2);
disp('state is 1')
else
yprime(4) = yprime(3);
disp('state is 2')
end
end
function [val,isterm,dir] = myEvents(t,y,State)
yprime = myFunction(t, y, State);
val = yprime(2) - yprime(3);
isterm = 1;
dir = 0;
end
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Risposte (1)
Jan
il 18 Mar 2021
y0 = [1,2,3,4];
t0 = 0;
tEnd = 42;
opt = odeset('Tol', 1e-8);
y = y0;
t = t0;
while t(end) < tEnd
if -y(2) > y(3)
State = 1;
else
State = 2;
end
opt = odeset('Events', @(t, y) myEvents(t, y, State));
fcn = @(t,y) myFunction(t, y, StaTe);
[at, ay] = ode45(fcn, [t(end), tEnd], y(end, :), opt);
t = cat(1, t, at(2:end));
y = cat(1, y, ay(2:end, :));
end
function myFunction(t, y, State)
if State == 1
... implement the first function
else
... implement the second function
end
end
function [value,isterminal,direction] = myEvents(t, y, State)
if State == 1
... implement the first function
else
... implement the second function
end
end
2 Commenti
Jan
il 20 Mar 2021
The event function does not influence the step size, but detects events. This is used to stop the integration and to change the state.
If e.g. the function to be integrated changes, when a component of the trajectory gets 0, this is detected in the event function.
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