Transc. Eqn - Symb. Iterative Sol'n.?

• To: mathgroup at smc.vnet.net
• Subject: [mg15639] Transc. Eqn - Symb. Iterative Sol'n.?
• From: Eric Strobel <EStrobel at schafercorp.com>
• Date: Sat, 30 Jan 1999 04:28:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Sorry for the abbreviations...

I think I'm just being dense and when I see the answer, I'll emit a
hearty  "DOH!!!", but here goes:

Problem: I *think* it should be relatively straightforward to write a
Block/ Module to do a symbolic Newton-Raphson (or similar such thing)
solution of a

transcendental equation.  But I just can't seem to figure out how to
write  it. [I've been using Mathematica for years, but never got into
programming...]  I'd  like to be able to have the Block serve as a
function, and have an input  specifying the number of iterations to do.

Example: The prototypical example would be Kepler's problem, M = E - e
Sin[E],
where M = mean anomaly, e = eccentricity and E = eccentric anomaly.  One
will
sometimes run across approximate solutions in powers of e, for e small
--  these are usually out to the e^2 or e^3 terms and appear to have
been done by
my suggested process (doing the first few iterations of a Newton sol'n.
symbolically).

I'm interested in being able to take this to higher orders, and for my
particular equation (of course).  I bring up Kepler's problem both
because it
is reminscent of mine, and because it might be of more general interest,
particularly to the college students among us.

Thanks.

- Eric.

```

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