Subject: Taylor series solution to diff eq. in maxima
From: Richard Fateman
Date: Sun, 06 Dec 2009 17:14:39 -0800
Someone may have written an equivalent program, but for sure you can use
deftaylor to define a taylor series Q with
arbitrary coefficients like q[0], q[1], ....
Then plug Q into your differential equation and solve, successively, for
q[0], q[1], etc.
There are fancier ways of setting this up, and ways of coming up with
the coefficients much faster.
I'm assuming that your equation can be solved by the method of Frobenius
or something similar.
Good luck
and then plugChris J Nassar (RIT Student) wrote:
> In mathematica I can solve a differential equation using a series
> approach using the following code...
>
> In[3]:= Derivative[N_][P][0] := D[P''[x], {x, N - 2}] /. x -> 0
> In[4]:= P''[x] = (1/P[x])*(P'[x])^2 + (P[x])^2*(A)) -P[x]*(B)
> In[5]:= P'[0] = 0
> In[6]:= P''[0] = P''[x] /. x -> 0
> In[7]:= PTAYLOR = Series[P[x], {x, 0, 3}]
>
>
> maxima complains about the first assignment...
>
> diff(p(x),x,2) : (1/p(x))*(diff(p(x),x))^2+p(x)^2*(A))-p(x)*(B));
>
> assignment: cannot assign to diff(p(x),x,2)
> -- an error. To debug this try: debugmode(true);
>
> How should I consider solving this equation in maxima?
>
> Thanks,
> Chris
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