Question on Initial value problem - error correction

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Question
I create a script
function f = exercise711 (t, x)
f = t * x.^2;
end
And on the command window, I wrote
>> [t1, x1] = ode45(@exercise711, [0 1], 1);
>> plot(t1, x1)
>> hold on
>> [t2, x2] = ode45(@exercise711, [0 2], 1);
Warning: Failure at t=1.414192e+00. Unable to meet integration tolerances
without reducing the step size below the smallest value allowed
(3.552714e-15) at time t.
In ode45 (line 308)
>> plot(t2, x2)
here, for the interval [0 2], I get an error and the graph is wrong. Why? How can I correct it? Please help me to do this question in a correct way.
Thanks a lot.

Accepted Answer

Ameer Hamza
Ameer Hamza on 24 Apr 2020
Edited: Ameer Hamza on 24 Apr 2020
The result is correct, and it was the purpose of the exercise to show that the solution of an ODE can diverge to infinity. If you use symbolic toolbox to solve this equation, you can see that the analytical solution of this ODE is
and at , there is a singularity and the output become infinity. You can see in warning message that the issue also occurs at 1.414... In the interval [0,1] there is no singularity and MATLAB does not give any warning.
  6 Comments
Ameer Hamza
Ameer Hamza on 7 May 2020
That question requires a bit of thinking. I will answer it if I get some ideas.
Zeynep Toprak
Zeynep Toprak on 7 May 2020
thanks a lot. In fact, very similart question is here
But, I am writing D1 matrix in wrong way. If I can correct it, this solution is valid, i think. Again, thank you for your consideration, and helping.

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