How to get from the first line to the second line? enter image description here

$$u_{n+1}(x,t) = u_n (x,t) - \int_0^t \left\{ (u_n)_s(x,s) - \frac{\partial}{\partial s} G(x,s) + \frac{\partial}{\partial s}E^{-1} \left\{ vE \left[ N u_n(x,s) \right] \right\} \right\}\, ds$$ Or alternatively $$ u_{n+1}(x,t) = G(x,t) - E^{-1} \left\{ vE \left[Nu_n (x,t) \right] \right\} $$

  • $\begingroup$ Is $(u_n)_s$the same as ${\partial \over \partial s} (u_n)$? $\endgroup$ – user617446 Jun 12 at 8:16
  • $\begingroup$ Yes, (un)s is the same as ∂∂s(un) $\endgroup$ – Pyh Jun 12 at 9:03
  • $\begingroup$ OK, so you are integrating a differential, $\int {d(F)\over dx} dx$ $\endgroup$ – user617446 Jun 12 at 10:19
  • $\begingroup$ can you prove to show me? $\endgroup$ – Pyh Jun 12 at 12:18

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