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How can I solve the following ODE numerically $$F'''+FF''+1-F'^2=0$$ $$F(0)=F'(0)=0\qquad F'(\infty)=1$$ Thank you.

Lutz Lehmann
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ak ve
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  • You could mention that this is one case of the Falkner-Skan equation. With that key word you can find topics like https://math.stackexchange.com/questions/158604/solve-falkner-skan-numerically, https://math.stackexchange.com/questions/3884444/falkner-skan-solution-using-a-tridiagonal-matrix, – Lutz Lehmann Nov 26 '20 at 19:58
  • The idea of a "far field approximation" like in https://math.stackexchange.com/questions/1610416/how-to-solve-an-ode-with-y-1-term could also be relevant, up to now I have not found a non-trivial application to this equation. – Lutz Lehmann Nov 26 '20 at 20:18

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Similar to How do you solve this kind of third order ODE?,

Let $U=(F')^2$ ,

Then $\pm\sqrt U\dfrac{d^2U}{dF^2}+F\dfrac{dU}{dF}-2U+2=0$

doraemonpaul
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