How to introduce a constraint and stop condition in ode45 ？

Question

Cola 2022-6-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1736205-how-to-introduce-a-constraint-and-stop-condition-in-ode45

编辑： Cola 2023-7-20

采纳的回答： Torsten

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There are two questions. The first question is how to introduce a constraint in ode45 for a variable.

For example, the constraint of y(2) is 0<=y(2)<=2 in the following code，and how to introduce it?

The second question is how to introduce a stop condition in ode45？

For example, how to stop the integration of ode45 at two conditions when y(1)<-1 and y(2)<-2 in the following code?

Please give me help. Thanks.

y10=2;
y20=0;
Y0=[y10,y20];
[t, Y] = ode45(@fun,[0:0.1:20], Y0);
plot(t,Y(:,1),'-o',t,Y(:,2),'-o')
xlabel('Time t');
ylabel('Solution y');
legend('y_1','y_2')
function Dy=fun(t,y)
Dy=zeros(2,1);
Dy(1)=y(2);
Dy(2)=(1-y(1)^2)*y(2)-y(1)
end

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Jan 2022-6-8

Note: [] is Matlab's operator for concatenations. [0:0.1:20] concates the vector 0:0.1:20 with nothing, so tzhe square brackets are a waste of time only.

Cola 2022-6-9

You have my gratitude.

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Answer 1

Torsten 2022-6-8

2
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https://ww2.mathworks.cn/matlabcentral/answers/1736205-how-to-introduce-a-constraint-and-stop-condition-in-ode45#answer_981350

编辑：Torsten 2022-6-8

First question:

You can't prescribe a constraint for a solution variable of an ODE. The ODE variable results automatically from the ODE equation, so you cannot influence it: either it respects your constraint or not.

Second question:

Use the "event" facility of the ODE integrators:

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

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Cola 2022-6-9

编辑：Cola 2023-7-20

Thank you so much. The second question is solved by the ''event''. The first question is just what you said, but I still want to try it.

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Answer 2

Jan 2022-6-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1736205-how-to-introduce-a-constraint-and-stop-condition-in-ode45#answer_981365

Both is done by an event function. There you can check the values of the current trajectory and stop the integration. If the values should be limited only, you restart the integration from the current location setting the corresponding derivative to 0.

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Cola 2022-6-9

Thank you for your prompt response. The second question is solved, and I am trying to introduce a constraint by an event function for the first question .

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