Why not to make differentiation in spectral space?
I don't see a problem in if maxima will differentiate directrly as well.
You will need go to numbers in any case either following to Galerkin
procedure, or estimating polynomials in collocation points (pseudospectral)
> I'm expanding a function in chebyshev polynomials and then substituting
> it into a differential equation. I get an expression that has noun forms
> for the derivatives. I would like to expand the derivatives without
> having maxima expand the chebyshev polynomials into their basic form.
> How can I make it do this?
>
> Example, I want to get %o199 where the derivatives have been evaluated
> according to the gradef properties of the chebyshev polynomials, not
> into a form that's a basic polynomial in x (apologies for the word
> wrapping in the last expression).
>
> ----
>
> (%i196) depends(foo,x);
> (%o196) [foo(x)]
> (%i197) foo = sum(A[i]*funmake(chebyshev_t,[i,x]),i,0,3);
> (%o197) foo = A T (x) + A T (x) + A T (x) + A T (x)
> 3 3 2 2 1 1 0 0
> (%i198) 'diff(foo,x)-3*'diff(foo,x,2) = 0;
> 2
> dfoo d foo
> (%o198) ---- - 3 ----- = 0
> dx 2
> dx
> (%i199) subst(%th(2),%th(1));
> d
> (%o199) -- (A T (x) + A T (x) + A T (x) + A T (x))
> dx 3 3 2 2 1 1 0 0
> 2
> d
> - 3 (--- (A T (x) + A T (x) + A T (x) + A T
> (x))) = 0
> 2 3 3 2 2 1 1 0 0
> dx
> (%i200)
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