MaplePrimes - answers and comments on Question, how to solve this equation?

NextZero

acer — Mon, 12 Nov 2012 10:57:33 Z

It's possible that the integral isn't being computed accurately enough for fsolve (which is basing its own accuracy demand on the value of Digits). I'm not yet sure whether that's the issue. But this seems to work,

restart:
F := Int(sqrt((2.138+0.3e-2*exp((4.2^2-z^2)/d^2))^2-2.141^2), z=0 .. 4.2) = .5:
f:=unapply((lhs-rhs)(F),d):

#plot(f,2.0..6.0);

RootFinding:-NextZero(f,2.0);

                          3.957142935

acer

By DirectSearch:-SolveEquations

Markiyan Hirnyk — Mon, 12 Nov 2012 12:45:32 Z

Download SolveEquations.mw

Thank you, Markiyan Hirnyk and

maple fan — Tue, 13 Nov 2012 06:18:20 Z

Thank you, Markiyan Hirnyk and acer.

Your methods are very useful.

To acer:

the NextZero command does resolve my problem.

but for the second method, commands is below:

(

restart:

F := Int(sqrt((2.138+0.3e-2*exp((4.2^2-z^2)/d^2))^2-2.141^2), z=0 .. 4.2,
digits=15, epsilon=1e-12, method=_d01ajc) = .5:

fsolve(F,d=2..6);
)

there still exists problem.

Usually my worksheet is in Worksheet Mode.

Unless I set the commands above Join Execution Groups, I wouldn't get the result(3.957142936).

xp 32, maple 13, Celeron 2.53GHz.

still need help.

fsolve

acer — Mon, 12 Nov 2012 11:10:23 Z

It seems my guess was right. fsolve is trying to nail down the 10th digit accurately (for default Digits=10 as the environment). So unless it can compute the expression (involving a numeric integral) at least that accurately then it may get into some trouble. And it may also hit a known issue where evalf/int goes "away" while trying to find discontinuities of the integrand in expression form and when no quadrature method is forced. Using the integrand in operator form is going to confuse fsolve which has overzealous checks for mixed operator/expression cases, so that leaves forcing the quadrature method.

conclusion: tighten the accuracy of the numeric integral, so fsolve has a chance to meeting its own (somewhat inflexible) accuracy requirement, and force the quadrature method to make it faster.

restart:

F := Int(sqrt((2.138+0.3e-2*exp((4.2^2-z^2)/d^2))^2-2.141^2), z=0 .. 4.2,
         digits=15, epsilon=1e-12, method=_d01ajc) = .5:

fsolve(F,d=2..6);

                          3.957142936

If you obtained that Int() call as the result of something else then you might have to do some `op` work to shoehorn in those extra options.

acer

AddOptions

Alejandro Jakubi — Mon, 12 Nov 2012 11:41:22 Z

@acer

Yes. I find that a command "AddOptions" is frequently needed. The counterpart of IntegrationTools:-StripOptions.

works for me

acer — Tue, 13 Nov 2012 07:13:27 Z

It worked for me, with or without separate execution groups, in Maple 13.02. See attached worksheet.

mmm.mw

You've shown a pair of round brackets around all the commands. I didn't have that in what I posted. What's their purpose?