Question on Initial value problem - error correction

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.

Answer 1

[Ameer Hamza]

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.

[Zeynep Toprak]

I see. Many thanks :)

[Ameer Hamza]

I am glad to be of help.

[Zeynep Toprak]

Dear Ameer Hamza, You solved my questions in very nice and understandable way. I have also a question. You know I try to learn by myself, and I dont know anyone to learn and to ask. please can you help me again?my question is here

[Zeynep Toprak]

Dear Hamza, I will be happy if you help me. Thanks a lot:)

[Ameer Hamza]

That question requires a bit of thinking. I will answer it if I get some ideas.

[Zeynep Toprak]

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.