how to solve ODE that contains integration over time?

Question

Gefen Baranes 2021-11-12

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https://ww2.mathworks.cn/matlabcentral/answers/1584999-how-to-solve-ode-that-contains-integration-over-time

回答： Bjorn Gustavsson 2021-11-12

Q_ODE.png

Hi,

I need to solve the attached ODE. I known how to handle with X as a matrix. My problem is the integral. How can I plug it inside the ODE45 solver? Is it possible on Matlab?

Thank you!

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Answer 1

Bjorn Gustavsson 2021-11-12

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For this type of integro-differential equations the standard "first-stab" trick is to differentiate it one step, which should give you the second-derivative of X on the LHS and something you can work out analytically for the RHS such that the integral will vanish when taking the limit of the RHS derivative. Then you'll have a system of second-order ODEs.

HTH