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These are questions asked by Saha

I need a help for solving this non linear equation by Adomian Decomposition Method.How to find A0,A1,A2... and u1,u2,u3 and a series.I am getting this error,Please help me.


PDEtools[declare](prime = x);

`derivatives with respect to`*x*`of functions of one variable will now be displayed with '`


equ1 := u[tt] = 1/2*(u[xx]+u[yy])+u^2:

ICS; u(x, y, 0) = 1, u[t](x, y, 0) = e^(x+y), lambda = 0, u[0] = 1+t*e^(x+y), F(u[0]) = u[0]^2

for n from 0 to 5 do A[n] := d^n*[F*(sum(lambda^i*u[i], i = 0 .. n))]/(factorial(n)*`dλ`^n); u[n+1] = (1/2)*int[diff(sum(u[n], n = 0 .. 5), x, x)+diff(sum(u[n], n = 0 .. 5), y, y), t = 0 .. t, t = 0 .. t, dt*dt]+int[A[n], t = 0 .. t, t = 0 .. t, dt*dt] end do



I need help to solve this ODE,

I didn't get series values F(k+3),Theta(k+2),phi(k+2),error comes in summation values.and

How to find the unknown parameters A,B,C.

Please Help,

I am trying to plot some movement equations, but the following error keeps happening:

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

when I tryed to rewrite the equation the error became:

Can someone help me with those errors?

Here is the code

Please Help!  The flow gets me like this,Where should i fix this problem.The flow changes for me fluctuate through the series range.What to do to get upflow in f(eta) and downflow in theta(eta)

 How to rectify the Error, (in MTM:-findsym) invalid input: a string/name list is expected for sort method `lexorder`   .Could you please help me to plot the curve.

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