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# ARRRRRRRRRRGH - horrible (and possibly unsolvable ) problem

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Urk. Don''t you hate those HORRIBLE problems? How would i solve I+(-bav*e^(bv)+a(1-e^(bv))) = 0 : a, I and b are constants (known). (e is of course exponent) This is , like , horrible... i am feeling suicidal already. What is worse, i have to write a program to solve this equation on an 8bit micro!!! yurk! (but let''s get to that barrier later ) Can this be solved? Or am i overlooking something REALLY obvious??

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Hi,

i think your equation is of the form xe^(x) = cte if v is the variable.
I don''t know if you can solve this one but with a computer you can find a solution with a dichotomi.

have a good day

Plotark

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the furthest i got was

ln(-I/A - 1) = BV + ln(-BV-1)

urk.

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That might help:
if f := x -> x*exp(x)
then f^(-1) is the Lambert Omega function:

http://mathworld.wolfram.com/LambertW-Function.html

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You can use taylor''s series:

For every x, e^x = 1 + x + (x^2)/(2!) + (x^3)/(3!)...

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Are you supposed to be solving it analytically and then using the computer as an oversized calculator or are you supposed to be programming a numerical method to solve it?

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quote:
Original post by beaton_john
What is worse, i have to write a program to solve this equation on an 8bit micro!!!

HAVE TO write it? Sounds like homework to me. Please review the Forum FAQ

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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If you don't need exact results you can do something as simple as interval halving aka bisection method. If this doesn't converge fast enough use a linear interpolation method (secant or regula falsi) or even newton's method. These are all pretty simple to progam even in asm.

There is only 1 zero I think so these will work nicely or should anyway =p

[edited by - O_o on March 1, 2004 7:54:25 PM]

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quote:
Original post by grhodes_at_work
quote:
Original post by beaton_john
What is worse, i have to write a program to solve this equation on an 8bit micro!!!

HAVE TO write it? Sounds like homework to me. Please review the Forum FAQ

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Though to be fair, he''s only asking for the mathematical solution, not the programming solution.

The way I (a complete non-mathematician) would do it is to have the computer guess millions of times per second. Start with some value of v, see if the answer gets closer or farther away from 0 as v rises, and then adjust v until the equation yields 0.001 or possibly something more accurate, and call it the solution. Voila! Hack math!

~CGameProgrammer( );

-- Upload up to four 1600x1200 screenshots of your projects, registration optional. View all existing ones in the archives..

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quote:
Original post by CGameProgrammer
Though to be fair, he''s only asking for the mathematical solution, not the programming solution.

That doesn''t matter. I don''t want people taking advantage of these forums to cheat on any school assignment.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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