Question on Initial value problem - error correction

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Zeynep Toprak 2020-4-24

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https://ww2.mathworks.cn/matlabcentral/answers/520508-question-on-initial-value-problem-error-correction

评论： Zeynep Toprak 2020-5-7

采纳的回答： Ameer Hamza

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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.

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采纳的回答

Ameer Hamza 2020-4-24

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https://ww2.mathworks.cn/matlabcentral/answers/520508-question-on-initial-value-problem-error-correction#answer_428192

编辑：Ameer Hamza 2020-4-24

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.