Problem 42891. Differential equation and events

Created by hubert andre

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You have to solve the non-linear time variant differential equation:<pre class="language-matlab">(cos(y)+2)*y''+atan(y)*sin(0.01*t)^2+y*sin(0.5*t)=0
</pre>with initial condition as input of the function<pre class="language-matlab">[y(0);y'(0)]=[a,b]
</pre>and return the time 'te' when 'y' crosses zero from the negatives values to the positive values.<pre class="language-matlab">te=zero_crossing(a,b)
</pre>tip: use the 'Events' option in odeset to detect the crossing, stop integration and get the time 'te'. See how to use it here : <a href = "http://www.mathworks.com/help/matlab/math/ode-event-location.html?searchHighlight=ballode">http://www.mathworks.com/help/matlab/math/ode-event-location.html?searchHighlight=ballode</a>Additional info:<ul><li>in the test case, the solver ode45 is used, with options 'RelTol'=1e-8 and 'AbsTol'=1e-10.</li><li>because you don't know in advance the final time of the crossing, you can solve again further in time if no crossing is detected, starting from the point of the final time of previous integration.</li></ul>

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Last Solution submitted on Jun 03, 2021

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Tim on 14 Jun 2016

It looks like [y;y']=[a,b] would mean y(0)=a and y'(0)=b, but a first order differential equation should have one initial condition y(t0)=y0.

hubert andre on 14 Jun 2016

Thanks Tim, yes, I did a mistake in the equation, its a 2nd order.

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