Please refer to paper "A modified parametric iteration method for solving nonlinear second order BVPs, link: http://www.scielo.br/pdf/cam/v30n3/a02v30n3. In example 5.1, i am unable to understand how u1(x) has been calculated. As it has been mentioned in Para 3 of paper that A[u(t)] in each iteration is expanded in Taylor series around 'a', here a = -1 for given problem.

I tried solving and expanding u''(t)-1/2exp(1/2(t+1)cos(u(t)-3t+7))= G(t) + O((t+1)^n+1) and my Go(t) comes out to be -1/2 - (t+1)/4. I plugged same in relation (23) i.e.governing equation for modified PIM but i am not getting same u1 as it has been calculated by you in paper i.e.

u1 = -10 + (3+1/2h)(x+1)- 1/4h(x+1)^2

Where is the mistake ? can someone please point out ? and moreover can anyone please elaborate a bit more on how to calculate u1.

Thanking you in anticipation.

Regards.

Saad Sharjeel