Please check the research paper regarding numerical solution of non linear 5th and 6th order BVP using Daftardar Jafari Method (section 6: numerical results, example 1)
http://www.hindawi.com/journals/jcengi/2014/286039/
In the given 5th order BVP, i am unable to understand how author has calculated u1?
As defined at (16) : uk+1=L-1[GK] where K>=0, to get u1 we set k=0,
u1=L-1[G0], all G's are defined at (4), G0=N(u0), where N is the nonlinear term of equation, in this case it is u2 , since it is a 5th order BVP , so L-1 is a 5 fold integral operator,
so u1=L-1[e-xG0] , the problem is; i have tried applying 5 fold integral on e-xu02,where u0 is given at (23), using mathematica , i am unable to get the results as given in paper as x5/120+....+O(x15). i have tried using limits 0 to x as well as 0 to 1 but results were different (even with simplification and full simplification). Can someone clearly identify where is my mistake ? Thanking in anticipation and best regards.