MaplePrimes - answers and comments on Question, Solving a complicated nonlinear equation numerically

a remark

Axel Vogt — Mon, 02 Jan 2012 01:49:22 Z

Roughly you want

6.6e18906*n*((-2.302585093+ln((-6.*n+7.*n*m+4.*n*t+8.-10.*t-10.*m)/(-2.*n+2.*n*m+n*t-3.*m-4.*t+3.)))/(.5e6990-.1e6990*n)
^(7447/10000)/m)^(10000/2753)*m +
690.7755279-.3e3*ln((-6.*n+7.*n*m+4.*n*t+8.-10.*t-10.*m)/(-2.*n+2.*n*m+n*t-3.*m-4.*t+3.)) = 0.

As it was said 6.6e18906 is likely to kill numerics - where you would have to supply concrete
values for m=taum and t=taut to work at all.

And symbolically I have doubts there are usable solutions.

Best would be to think about appropriate scaling of variables, which you have to do before
arriving at your final task.

Just as thoughts

Smoothed-out code

Markiyan Hirnyk — Mon, 02 Jan 2012 17:19:07 Z

This should work in Maple 14 or 15:
Digits := 20;
EQN := 5.915635290*10^18905*n*(ln(expand(.1974600000*(4.137221948*10^9-3.187977881*10^9*n+
3.579712132*10^9*n*taum+2.049414400*10^9*n*taut-5.560674900*10^9*taum-5.560674900*10^9*taut))/
(-2.065539727*10^9*n+2.333329620*10^9*n*taum+1.372164917*10^9*n*taut+2.519530558*10^9-
3.492604298*10^9*taum-3.723094273*10^9*taut))/((5.012372749*10^6989-
1.379404981*10^6989*n)^evalf(7447/10000)*taum))^evalf(10000/2753)-319.9820565*
ln((19746.*(4.137221948*10^11-3.187977881*10^11*n+3.579712132*10^11*n*taum+
2.049414400*10^11*n*taut-5.560674900*10^11*taum-5.560674900*10^11*taut))/
(-2.065539727*10^16*n+2.333329620*10^16*n*taum+1.372164917*10^16*n*taut+
2.519530558*10^16-3.492604298*10^16*taum-3.723094273*10^16*taut))/taum = 0;
#smoothed-out code: expand in logarithm and evalfed exponents
UUU := solve(EQN, n, useassumptions)assuming 0 < taut, taut < 1, taum > 0, taum < 1;

Enquiry: Smoothed-out code can't work now for the same equation

yewslyewsl — Tue, 03 Jan 2012 11:29:55 Z

Hi,

When I first tried to solve the equation, EQN, by following the method below, it worked, ie., EQN can be solved. But when I tried to solve the same equation again using the same method as below, the equation EQN, cannot be solved now! I wonder why. It is strange.

Digits := 20;
EQN := 5.915635290*10^18905*n*(ln(expand(.1974600000*(4.137221948*10^9-3.187977881*10^9*n+
3.579712132*10^9*n*taum+2.049414400*10^9*n*taut-5.560674900*10^9*taum-5.560674900*10^9*taut))/
(-2.065539727*10^9*n+2.333329620*10^9*n*taum+1.372164917*10^9*n*taut+2.519530558*10^9-
3.492604298*10^9*taum-3.723094273*10^9*taut))/((5.012372749*10^6989-
1.379404981*10^6989*n)^evalf(7447/10000)*taum))^evalf(10000/2753)-319.9820565*
ln((19746.*(4.137221948*10^11-3.187977881*10^11*n+3.579712132*10^11*n*taum+
2.049414400*10^11*n*taut-5.560674900*10^11*taum-5.560674900*10^11*taut))/
(-2.065539727*10^16*n+2.333329620*10^16*n*taum+1.372164917*10^16*n*taut+
2.519530558*10^16-3.492604298*10^16*taum-3.723094273*10^16*taut))/taum = 0;
#smoothed-out code: expand in logarithm and evalfed exponents
UUU := solve(EQN, n, useassumptions)assuming 0 < taut, taut < 1, taum > 0, taum < 1;

Thanks in advance for any kind advice!

Suggestion

Markiyan Hirnyk — Wed, 04 Jan 2012 12:04:50 Z

@yewslyewsl My explanation is the following: such Maple commands as solve, dsolve, limit, and int can produce different outputs in different executions and sessions. For example, look at the recent post
http://www.mapleprimes.com/questions/128885-Dsolve-Boundary-Condition-On-Infinity#comment128886
Unfortunately, I don't see a workaround for this.