# I have a question about Elzaki variational iteration method.

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 $$u_{n+1}(x,t) = G(x,t) - E^{-1} \left\{ vE \left[Nu_n (x,t) \right] \right\}$$

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