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Question: adomian polynomial for nolinear function

Question:adomian polynomial for nolinear function

usmanjutt 15 Maple
differentiation summation duplicate-question
October 15 2020
1

i have two nonlinear functions from which one is exicuted properly but 2nd funnction not risponde properly. i can not understan how to overcome it
 

> 

restart
> 

with(LinearAlgebra):
> 

> 

F := proc (x) options operator, arrow; x^2 end proc:
> 

F(u(t));

u(t)^2

 (1)
> 

G := proc (w) options operator, arrow; w*dw/dt end proc:
> 

G(h(t));

h(t)*dw/dt

 (2)
> 

for n from 0 while n <= 6 do V[n] := (diff(F(sum(t^i*u[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n); U[n] := (diff(G(sum(t^i*h[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n) end do:
> 

t := 0;

0

 (3)
> 

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

u[0]^2

  

h[0]*dw/dt

  

2*u[0]*u[1]

  

h[1]*dw/dt

  

2*u[0]*u[2]+u[1]^2

  

h[2]*dw/dt

  

2*u[0]*u[3]+2*u[1]*u[2]

  

h[3]*dw/dt

  

2*u[0]*u[4]+2*u[1]*u[3]+u[2]^2

  

h[4]*dw/dt

  

2*u[0]*u[5]+2*u[1]*u[4]+2*u[2]*u[3]

  

h[5]*dw/dt

  

2*u[0]*u[6]+2*u[1]*u[5]+2*u[2]*u[4]+u[3]^2

  

h[6]*dw/dt

 (4)
> 

for j from 0 while j <= n-1 do u[0] := 1; u[j+1] := int(x*B[j], x)+int(A[j], x) end do;

1

  

(1/2)*x^2*h[0]*dw/dt+x

  

1

  

(1/2)*x^2*h[1]*dw/dt+(1/3)*x^3*h[0]*dw/dt+x^2

  

1

  

(1/2)*x^2*h[2]*dw/dt+(1/3)*x^3*h[1]*dw/dt+(5/12)*x^4*h[0]*dw/dt+x^3+(1/20)*h[0]^2*dw^2*x^5/dt^2

  

1

  

(1/2)*x^2*h[3]*dw/dt+(1/3)*x^3*h[2]*dw/dt+(1/6)*x^4*h[1]*dw/dt+(1/6)*x^5*h[0]*dw/dt+(1/2)*x^4+(13/180)*h[0]^2*dw^2*x^6/dt^2+(2/5)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^5+(1/2)*((1/2)*h[1]*dw/dt+1)*x^4

  

1

  

(1/2)*x^2*h[4]*dw/dt+(1/3)*x^3*h[3]*dw/dt+(5/12)*x^4*h[2]*dw/dt+(1/15)*x^5*h[1]*dw/dt+(1/18)*x^6*h[0]*dw/dt+(1/5)*x^5+(139/1260)*h[0]^2*dw^2*x^7/dt^2+(2/15)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^6+(1/5)*((1/2)*h[1]*dw/dt+1)*x^5+(1/160)*h[0]^3*dw^3*x^8/dt^3+(1/3)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^6+(2/5)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^5+(1/9)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^6/dt+(1/5)*((1/2)*h[1]*dw/dt+1)^2*x^5

  

1

  

(1/2)*x^2*h[5]*dw/dt+(1/3)*x^3*h[4]*dw/dt+(5/12)*x^4*h[3]*dw/dt+(1/6)*x^5*h[2]*dw/dt+(1/45)*x^6*h[1]*dw/dt+(1/63)*x^7*h[0]*dw/dt+(139/5040)*h[0]^2*dw^2*x^8/dt^2+(17/1296)*h[0]^3*dw^3*x^9/dt^3+(1/15)*x^6+(4/105)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^7+(1/15)*((1/2)*h[1]*dw/dt+1)*x^6+(2/21)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(2/15)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^6+(1/15)*((1/2)*h[1]*dw/dt+1)^2*x^6+(1/4)*((13/180)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^8+(2/7)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*((5/12)*h[1]*dw/dt+1+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(2/5)*((1/3)*h[2]*dw/dt+(1/4)*h[0]*dw^2*h[3]/dt^2)*x^5+(1/4)*((1/20)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(5/36)*h[0]^2*dw^2/dt^2)*x^8+(2/7)*((5/12)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/3)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*(((1/2)*h[1]*dw/dt+1)*((1/3)*h[1]*dw/dt+1)+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(1/5)*((1/2)*h[1]*dw/dt+1)*h[2]*dw*x^5/dt+(2/63)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^7/dt

  

1

  

(1/20)*h[2]^2*dw^2*x^5/dt^2+(1/3)*x^3*h[5]*dw/dt+(5/12)*x^4*h[4]*dw/dt+(1/6)*x^5*h[3]*dw/dt+(1/18)*x^6*h[2]*dw/dt+(2/315)*x^7*h[1]*dw/dt+(1/252)*x^8*h[0]*dw/dt+(139/22680)*h[0]^2*dw^2*x^9/dt^2+(2167/90720)*h[0]^3*dw^3*x^10/dt^3+(7/8800)*h[0]^4*dw^4*x^11/dt^4+(1/2)*x^2*h[6]*dw/dt+(2/105)*x^7+(2/9)*((13/180)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(1/3)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^9+(1/4)*(((1/2)*h[1]*dw/dt+1)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)+(1/3)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^8+(2/7)*(((1/2)*h[1]*dw/dt+1)*((5/12)*h[1]*dw/dt+1)+(1/9)*h[0]*dw^2*h[2]/dt^2)*x^7+(1/3)*((1/3)*((1/2)*h[1]*dw/dt+1)*h[2]*dw/dt+(1/6)*h[0]*dw^2*h[3]/dt^2)*x^6+(1/105)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^8+(2/105)*((1/2)*h[1]*dw/dt+1)*x^7+(1/42)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^8+(4/105)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^7+(2/105)*((1/2)*h[1]*dw/dt+1)^2*x^7+(1/18)*((13/180)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^9+(1/14)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^8+(2/21)*((5/12)*h[1]*dw/dt+1+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^7+(2/15)*((1/3)*h[2]*dw/dt+(1/4)*h[0]*dw^2*h[3]/dt^2)*x^6+(1/18)*((1/20)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(5/36)*h[0]^2*dw^2/dt^2)*x^9+(1/14)*((5/12)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/3)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^8+(2/21)*(((1/2)*h[1]*dw/dt+1)*((1/3)*h[1]*dw/dt+1)+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^7+(1/9)*((1/10)*((1/3)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(25/144)*h[0]^2*dw^2/dt^2)*x^9+(1/8)*((1/20)*h[2]*dw^3*h[0]^2/dt^3+(5/6)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^8+(1/7)*((5/12)*h[0]*dw^2*h[2]/dt^2+((1/3)*h[1]*dw/dt+1)^2)*x^7+(2/9)*((139/1260)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((43/180)*h[0]*dw/dt+(8/45)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/6)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)/dt)*x^9+(1/4)*((43/180)*h[0]*dw/dt+(8/45)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/6)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((3/10)*h[1]*dw/dt+4/5+(1/10)*h[0]*dw^2*h[2]/dt^2+(1/5)*((1/2)*h[1]*dw/dt+1)^2)/dt)*x^8+(2/7)*((3/10)*h[1]*dw/dt+4/5+(37/120)*h[0]*dw^2*h[2]/dt^2+(1/5)*((1/2)*h[1]*dw/dt+1)^2)*x^7+(1/3)*((5/12)*h[2]*dw/dt+(1/6)*h[0]*dw^2*h[3]/dt^2)*x^6+(2/5)*((1/3)*h[3]*dw/dt+(1/4)*h[0]*dw^2*h[4]/dt^2)*x^5+(1/5)*((1/2)*h[1]*dw/dt+1)*h[3]*dw*x^5/dt+(1/15)*((1/2)*h[1]*dw/dt+1)*h[2]*dw*x^6/dt+(1/126)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^8/dt+(1/6)*h[2]*dw*((1/3)*h[1]*dw/dt+1)*x^6/dt

 (5)
> 

y := sum(u[l], l = 0 .. n-1);

1+(1/2)*x^4+(1/5)*x^5+(1/2)*x^2*h[0]*dw/dt+(1/2)*x^2*h[1]*dw/dt+(1/3)*x^3*h[0]*dw/dt+(1/2)*x^2*h[2]*dw/dt+(1/3)*x^3*h[1]*dw/dt+(5/12)*x^4*h[0]*dw/dt+(1/20)*h[0]^2*dw^2*x^5/dt^2+(1/2)*x^2*h[3]*dw/dt+(1/3)*x^3*h[2]*dw/dt+(1/6)*x^4*h[1]*dw/dt+(1/6)*x^5*h[0]*dw/dt+(13/180)*h[0]^2*dw^2*x^6/dt^2+(1/2)*x^2*h[4]*dw/dt+(1/3)*x^3*h[3]*dw/dt+(5/12)*x^4*h[2]*dw/dt+(1/15)*x^5*h[1]*dw/dt+(1/18)*x^6*h[0]*dw/dt+(139/1260)*h[0]^2*dw^2*x^7/dt^2+(1/160)*h[0]^3*dw^3*x^8/dt^3+(1/2)*x^2*h[5]*dw/dt+(1/3)*x^3*h[4]*dw/dt+(5/12)*x^4*h[3]*dw/dt+(1/6)*x^5*h[2]*dw/dt+(1/45)*x^6*h[1]*dw/dt+(1/63)*x^7*h[0]*dw/dt+(139/5040)*h[0]^2*dw^2*x^8/dt^2+(17/1296)*h[0]^3*dw^3*x^9/dt^3+x+(1/15)*x^6+x^3+(2/15)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^6+(1/15)*((1/2)*h[1]*dw/dt+1)^2*x^6+(1/4)*((13/180)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^8+(2/7)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*((5/12)*h[1]*dw/dt+1+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(2/5)*((1/3)*h[2]*dw/dt+(1/4)*h[0]*dw^2*h[3]/dt^2)*x^5+(1/4)*((1/20)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(5/36)*h[0]^2*dw^2/dt^2)*x^8+(2/7)*((5/12)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/3)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*(((1/2)*h[1]*dw/dt+1)*((1/3)*h[1]*dw/dt+1)+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(4/105)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^7+(1/15)*((1/2)*h[1]*dw/dt+1)*x^6+(2/21)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(2/15)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^6+(1/5)*((1/2)*h[1]*dw/dt+1)*x^5+(1/3)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^6+(2/5)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^5+(1/5)*((1/2)*h[1]*dw/dt+1)^2*x^5+(2/5)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^5+(1/2)*((1/2)*h[1]*dw/dt+1)*x^4+(1/5)*((1/2)*h[1]*dw/dt+1)*h[2]*dw*x^5/dt+(2/63)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^7/dt+(1/9)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^6/dt+x^2

 (6)
> 

``
> 

NULL


 

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