@janhardo they delete a lot i have other question too but no one answer this, i think is easy for them becuase even program is write in front of them but why they don't envolve, i have other post question but i need this adomian polynomial i have  other  coding but is not usfull for all function , i think this will be answer for all of kind function but how do by procedure and make a good design for it , i think this question will remain  becuase is hard to write program 

@Alfred_F in type two dont have direvitive i think i solve the first one two but step is two much i need someone to reduce my step in procedure i take to much time like that i need speed 

@acer  why didn't tell me before that u am new where i should know this i will post 1000 question like that without deleting i didn't post a questions becuase of that i  have a lot question but there is no one can answer this is problem
thank you sir and sorry if i disrespect in any kind 

@Alfred_F  the painleve  have first derivative with degree two i think is different , also this one must have a technique , maple must have a way to solve this kind of approximating solution easily more than other program i have to find best way calculating ODE and PDE by this LDM

@one man  the reason is that they say the question is same to the last question, they right is same topic but not same question they say i must add to that question and add to that question i posted a weak before like that no one see new update in question, today they delete more then 4 post of mine all of them are different, different algorithm and i spend time to post thus and waiting for answer otherwise if i know thus answer why i should ask in here .

@janhardo moderator did
is not just two he did atmost 10 of my questions i will upload the algorithm really i am need that

@acer this topic i didn't reach my final results this is done... the other question is so different how you delete my question with saying that is repeat question the algorithm is not solving equation and a minut ago that ODE is so different  open your eyes

@acer you think is repeated becuase thus picture i upload for undrestanding

@acer instead of help you delete my post it is a minut for you to write that algorithm

@janhardo i am stuck at this topic and more equation i have to solve it and really i am stuck badly but becuase of them stuf of mapleprime i can't ask my question they will delete

@janhardo after i finish my work i will ask a lot question about this topic i will try to solve a lot of example but i need an elite to combine my code and make a better design thanks for you.

@janhardo ......................................

@janhardo

@janhardo the mistake is here, when we define adomian my adomian is wrong, how   becuase for equation one A[0]=invlaplace[1/s*laplace(v[0]w[0])] i can't define be two function w and v becuase we have initial condition for u[0] v[0] and w[0] in finding u[1] we use v[0] and w[0] in finding v[1] we use u[0] and w[0] in finding w[1] we use u[0] and v[0] !

the equation is true but i did another mistake in adomian which we take derivative adomian for finding u(x,y,t) the nonlinear term diff(v,x) *diff(w,x) is like that diff(v,x)*diff(w,y) also for v(x,y,t) and w(x,y,t) it is clear in picture and also in mw.

@janhardo you are work hard on it, i have shame if i ask you another question about  this topic, is so intrested and so fun if  undrestand each part in this adomian it is  a minut for you but for me is so hard, for second example i did each part but this adomian make a problem for me i can't make it true with two diferent function if have time just look at  it if intrested give me a hand, hhh ofcurse you did all of this tahnks again..

adomian have a lot rule to written i have some other but this is easiest one but can't apply it for all function

ex2.mw