## 15 Reputation

4 years, 338 days

## Differential Transform Method...

Sorry for that

These are the initial conditions

F[0]:=0:F[1]:=1:F[2]:=a:Theta[0]:=b:Theta[1]:=-1: G[0]:=beta: G[1]:=K[s]*beta: delta(-1):=0: delta(0):=1:for k from 1 to 10 do delta(k):=0:od:A:=1:B:=1:C:=1:

F[k+3] := solve((k+1)*(k+2)*(k+3)*F[k+3]+2*nu*(sum(delta(k-m-1)*(m+1)*(m+2)*(m+3)*F[m+3], m = 0 .. k))+2*nu*(k+1)*(k+2)*F[k+2]+A*(sum(F[k-m]*(m+1)*(m+2)*F[m+2], m = 0 .. k))-A*(sum((k-m+1)*(m+1)*F[k-m+1]*F[m+1], m = 0 .. k))-B*M*(k+1)*F[k+1], F[k+3])

Theta[k+2] := solve(C*(k+1)*(k+2)*Theta[k+2]+2*nu*C*(sum(delta(k-m-1)*(m+1)*(m+2)*Theta[m+2], m = 0 .. k))+2*nu*C*(k+1)*Theta[k+1]+Pr*(sum(F[k-m]*(m+1)*Theta[m+1], m = 0 .. k))-Pr*(sum(Theta[k-m]*(m+1)*F[m+1], m = 0 .. k)), Theta[k+2])

G[k+2] := solve((k+1)*(k+2)*G[k+2]+2*nu*(sum(delta(k-m-1)*(m+1)*(m+2)*G[m+2], m = 0 .. k))+2*nu*(k+1)*G[k+1]+Sc*(sum(F[k-m]*(m+1)*G[m+1], m = 0 .. k))-lambda*Sc*G[k]+2*lambda*Sc*(sum(G[k-m]*G[m], m = 0 .. k))-lambda*Sc*(sum(sum(G[t]*G[m]*G[k-m-t], m = 0 .. k-t), t = 0 .. k)), G[k+2])

where Pr=6.2,M=2,nu=0.3,phi=0.05 and lambda=Sc=Ks=1

## Thank you...

@tomleslie Thank you for your timely help

## DTM...

@acer Sir,I have attached the work sheet,please check it over.To this equation i need to plot for different values wihch it is given as subs term