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From: Riccardo on 7 Apr 2010 12:23
"Steven Lord" <slord(a)mathworks.com> wrote in message <hpi4ec$e9a$1(a)fred.mathworks.com>...
>
> "kumar vishwajeet" <kwzeet(a)gmail.com> wrote in message
> news:hpgqjn$gv4$1(a)fred.mathworks.com...
> > "kumar vishwajeet" <kwzeet(a)gmail.com> wrote in message
> > <hpgovk$pd4$1(a)fred.mathworks.com>...
> >> TideMan <mulgor(a)gmail.com> wrote in message
> >> <b94018b6-814f-473c-8316-990881bdac94(a)w17g2000yqj.googlegroups.com>...
> >> > On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...(a)gmail.com> wrote:
> >> > > TideMan <mul...(a)gmail.com> wrote in message
> >> > > <b787b93d-3173-4ca1-9a48-d75f6afa6...(a)r1g2000yqb.googlegroups.com>...
> >> > > > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...(a)gmail.com> wrote:
> >> > > > > Does anyone know about differential operator in MATLAB
> >> > > > > corresponding to "D" operator in Mathematica. I am not looking
> >> > > > > for diff() function. I just want to use d/dt corresponding to
> >> > > > > "d/dx" used in mathematica. I want to use this "d/dt" operator in
> >> > > > > Bessel function:
> >> > > > > 1+sigma*D/alpha^2
> >> > > > > where D is the differential opeartor "d/dt"
> >> > >
> >> > > > I know nothing about Mathematica, but to numerically differentiate
> >> > > > in
> >> > > > Matlab, use:
> >> > > > help diff
> >> > > > help gradient
> >> > >
> >> > > > BTW, your equation makes no sense to me.
> >> > > > By my way of reckoning, D must have an argument of some sort.
> >> > >
> >> > > A bessel function ratio is defined as following:
> >> > > B = 1
> >> > > for ctr = 1:inf %here inf can be replaced with any finite number for
> >> > > approximation
> >> > > num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
> >> > > den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
> >> > > B = B*num/den
> >> > > end
> >> > >
> >> > > alpha0 and alpha1 are zeros of zero - order and first order bessel
> >> > > function.
> >> > > The final value of B is the bessel function ratio that I am trying to
> >> > > calculate.
> >> >
> >> > So when you write:
> >> > D/(alpha1(ctr)*alpha1(ctr))
> >> > you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
> >> > you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
> >> > t.
> >> > Is that correct?
> >> > If so, that's pretty weird notation.
> >> >
> >> > And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
> >> > numerically or symbolically?
> >>
> >> No I am not trying to divide or differentiate (alpha1(ctr)*alpha1(ctr)).
> >> The following expansion will make it clear:-
> >> 1+a1*d/dx+a2*(d/dx)^2+a3*(d/dx)^3+a4*(d/dx)^4+...........till infinity
> >> can be written as:
> >> 1+a1*D+a2*D+a3*D+................ till infinity
> >> where ai = sigma/(alpha1(ctr)*alpha1(ctr))
> >> So I am trying to find a replacement for D in MATLAB.
> >
> > Sorry..I mean
> > 1+a1*D+a2*D^2+a3*D^3+................ till infinity
>
> You can't have just a "naked" derivative operator -- you have to apply it to
> some function. If you have a symbolic function created using Symbolic Math
> Toolbox, then DIFF is the correct function to use ... as long as you use it
> on a sym object, which will invoke the DIFF _method_ for sym objects rather
> than the numeric DIFF _function_ which computes a difference.
>
> syms t
> f = sin(t)+cos(t);
> derivative = f; % the "0th" derivative is F itself
> n = 20;
> a = 1:n;
> total = sym(ones(1, n+1));
> for k = 1:n
> derivative = diff(derivative, t);
> total(k+1) = a(k)*derivative;
> end
> sumOfDerivatives = sum(total)
>
> Note I've done it this way so you can see each term that contributes to the
> sum -- if you want you can simply add each term to the running total inside
> the loop.
>
> Note that if you want you could put this code in a function that accepts f
> and the symbolic variable with which to differentiate; that way you could
> apply it like the "naked" (1+sum(a(k)*D^k)) operator you described above.
>
> --
> Steve Lord
> slord(a)mathworks.com
> comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
>

Perhaps the OP question can be rephrased as "can I do Operational Calculus in Matlab?".
I'd say the Symbolic Math Toolbox should be a decent candidate for that.
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