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Your equation can be re-written as a difference equation, if g(t) is the flow of f(x) then $$g(t+2)=g(t)+g(t+1)^2$$ or $$\Delta^2 g-(\Delta g+g)^2+2\Delta g-2g=0$$ This It is second order non-linear ordinary difference equation. It looks weird but at least you can try to apply methods of discrete calculus to this equation (with not much hope though). |
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Your equation can be re-written as a difference equation, if g(t) is the flow of f(x) then $$g(t+2)=g(t)+g(t+1)^2$$ or $$\Delta^2 g-(\Delta g+g)^2+2\Delta g-2g=0$$ This looks weird but at least you can try to apply methods of discrete calculus to this equation (with not much hope though). |
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