Dear Prof. Meade,

Thanks for your very useful reply and comments. I would like to respond in the following way:

Q: Why do you stop after 10 iterations? why not more? or fewer?

10 was a good number that gave me converged value of u, when I expanded the RHS of the differential equation upto first order using the Taylor's series (i.e. A/(1-u)^2 approx equal to A(1+2*u)). I did this in Matlab.  This wokrs fine for very small values of A which also implies very small values of u. If A is increased, u will also increase and hence we need more terms in the Taylor's approximation. However, Matlab had prolem with the computation time. So as a starting point I used the number 10 even with more terms in the Taylor's expansion. However, more iterations would definitely be required for high values of A.

Qs: What do you hope to be able to do with the expression that you obtain from this iteration? Are you interested in the behavior in terms of the parameter A, or in the coefficients of powers of x (and sin(x) and cos(x))?

I am ultimately interested in ploting the response of u as a function of x for various values of A.

Q: Do you need to keep the sin(x) and cos(x), or would you be satisfied with a series expansion in powers of x?

I think that It should be fine working with the truncated expansions of trigonometric terms. I will do some numerical experiments to consolidate this statement.

-------------------------

I will try with the collect option you have suggested.

Do you know any analogus thing in MATLAB? Please let me know, if same operation is possible in MATLAB with the collect option.

Thanks a lot for your valuable inputs.

-Manish

Hi Alec,

Thanks for the reply.

As such I do not know the estimated length. The resulting solution is an (truncated) anlytical solution of a nonlinear differential equation,

u''+u=A/(1-u)^2 with initial conditions u(0)=u'(0)=1.

We need more terms (in a loop) for achieving the convergence so I was trying with this method.

--Manish