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Question: how do i solve adomian polynomials

Question:how do i solve adomian polynomials

usmanjutt 15 Maple
differentiation
September 30 2020
2

when i solve adomian polynomials there is a derivative withrespect to t and then put t is equal to zero. now i have to find the dervative of function with respect to t but it is already equals to zero. and i change the variable the Df could not b solved.
 

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restart
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with(LinearAlgebra):
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F(u[i]) := u[i]^2:
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NULL
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for n from 0 while n <= 6 do F(u[n]) := x[n]^2; V[n] := (diff(F(sum(t^i*u[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n) end do:
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t := 0;

0

 (1)
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for i from 0 while i <= n-1 do A[i] := V[i] end do;

x[0]^2

  

(D(F))(u[0])*u[1]

  

(1/2)*((D@@2)(F))(u[0])*u[1]^2+(D(F))(u[0])*u[2]

  

(1/6)*((D@@3)(F))(u[0])*u[1]^3+((D@@2)(F))(u[0])*u[1]*u[2]+(D(F))(u[0])*u[3]

  

(1/24)*((D@@4)(F))(u[0])*u[1]^4+(1/2)*((D@@3)(F))(u[0])*u[1]^2*u[2]+(1/2)*((D@@2)(F))(u[0])*u[2]^2+((D@@2)(F))(u[0])*u[1]*u[3]+(D(F))(u[0])*u[4]

  

(1/120)*((D@@5)(F))(u[0])*u[1]^5+(1/6)*((D@@4)(F))(u[0])*u[1]^3*u[2]+(1/2)*((D@@3)(F))(u[0])*u[1]*u[2]^2+(1/2)*((D@@3)(F))(u[0])*u[1]^2*u[3]+((D@@2)(F))(u[0])*u[2]*u[3]+((D@@2)(F))(u[0])*u[1]*u[4]+(D(F))(u[0])*u[5]

  

(1/720)*((D@@6)(F))(u[0])*u[1]^6+(1/24)*((D@@5)(F))(u[0])*u[1]^4*u[2]+(1/4)*((D@@4)(F))(u[0])*u[1]^2*u[2]^2+(1/6)*((D@@4)(F))(u[0])*u[1]^3*u[3]+(1/6)*((D@@3)(F))(u[0])*u[2]^3+((D@@3)(F))(u[0])*u[1]*u[2]*u[3]+(1/2)*((D@@3)(F))(u[0])*u[1]^2*u[4]+(1/2)*((D@@2)(F))(u[0])*u[3]^2+((D@@2)(F))(u[0])*u[2]*u[4]+((D@@2)(F))(u[0])*u[1]*u[5]+(D(F))(u[0])*u[6]

 (2)
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> 

NULL


 

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