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how to solve a non linear ode equation ?

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hamza karim
hamza karim on 14 Sep 2021
Commented: Bjorn Gustavsson on 16 Sep 2021
Hello,
i have the following ODE that i want to solve
where k_r and kaq are constant values.
i am really stuck on what approach should i take to implement the equation in matalb, i have tried to linearize the equation using odetovectorfield function to solve it using ode45 or another solver but it won't work since the equation is not a quasi-linear differential equation as explained in the function description.
I would be grateful for any guidance or help
thanks in advance !

Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 14 Sep 2021
You have a quadratic equation for dCAdt, solve that one as a standard quadratic equation, you will end up with two solutions for dCAdt that will be possible to solve. If you're somewhat lucky you might end up with solutions that are simple enough to solve analyticalls. Depending on your initial condition you might have to discard one of the solutions and select one to proceed with.
HTH
  4 Comments
Bjorn Gustavsson
Bjorn Gustavsson on 16 Sep 2021
Regarding units again: you might have forgotten to correct reaction-rates from cm³/s to m³/s or some such easy to forget step. That would give you something like a 6 orders of magnitude change in reaction-rates, but would be hard to capture with dimensional analysis...

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