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.