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#### numerical solution to a set of non-liner equations

Hi, Maple experts,

I have two non-linear equations as follows:

tau := 1 - (1-p)^(1/9);

tau := 2(1-2*p)/ ((1-2*p)*33 + p*32*(1-(2*p)^5));

p and tau are both on the interval of (0,1), and we know there is a unique
(p, tau) pair solution.

Which Maple function/command can be used to solve the above two equations?
I have tried "solve" but it doesn't work.

Xinhua

 0
Xinhua
2/1/2005 2:54:37 AM
comp.soft-sys.math.maple 4344 articles. 3 followers.

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In article <ctmr3f$b1g$1@rumours.uwaterloo.ca>,
Xinhua Ling <x2ling@bbcr.uwaterloo.ca> wrote:

|>I have two non-linear equations as follows:

|>tau := 1 - (1-p)^(1/9);

|>tau := 2(1-2*p)/ ((1-2*p)*33 + p*32*(1-(2*p)^5));

These are not equations, they are assignments.  This is not what you
want, you want tau to be a variable.  You're also missing the "*"
after the first 2 in the second equation.

|>p and tau are both on the interval of (0,1), and we know there is a
unique
|>(p, tau) pair solution.

|>Which Maple function/command can be used to solve the above two
equations?
|>I have tried "solve" but it doesn't work.

The command for numerical solution of an equation or a system of
equations is "fsolve".  The "solve" command does symbolic
(closed-form) solutions.  Actually it does work in this case if
you do it properly.

> eqs:= {tau = 1 - (1-p)^(1/9),
tau = 2*(1-2*p)/ ((1-2*p)*33 + p*32*(1-(2*p)^5))};

> fsolve(eqs,{tau=0..1,p=0..1});

{tau = 0.03730507995, p = 0.2897714582}

> solve(eqs union {tau>0,tau<1,p>0,p<1});

9          18
{tau = 1 - (RootOf(1023 - 1025 _Z - 4128 _Z  + 7104 _Z

27          36         45          10          19
- 6272 _Z   + 2816 _Z   - 512 _Z   + 4128 _Z   - 7104 _Z

28          37         46               9 (1/9)
+ 6272 _Z   - 2816 _Z   + 512 _Z  , 0.9626949200) )     , p

9          18
= 1 - RootOf(1023 - 1025 _Z - 4128 _Z  + 7104 _Z

27          36         45          10          19
- 6272 _Z   + 2816 _Z   - 512 _Z   + 4128 _Z   - 7104 _Z

28          37         46               9
+ 6272 _Z   - 2816 _Z   + 512 _Z  , 0.9626949200) }

> evalf(%, 30);

{p = 0.289771458222600677923267166561,

tau = 0.037305079954568141337854862393}

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada
 0
israel
2/1/2005 5:41:01 AM
"Xinhua Ling" <x2ling@bbcr.uwaterloo.ca> writes:

> I have two non-linear equations as follows:
>
> tau := 1 - (1-p)^(1/9);
>
> tau := 2(1-2*p)/ ((1-2*p)*33 + p*32*(1-(2*p)^5));
>
> p and tau are both on the interval of (0,1), and we know there is a unique
> (p, tau) pair solution.
>
> Which Maple function/command can be used to solve the above two equations?
> I have tried "solve" but it doesn't work.

You want to use fsolve.  However, your second equation is not well-formed,
it is missing the multiplication symbol after the 2.

eq1 := tau = 1 - (1-p)^(1/9):
eq2 := tau = 2*(1-2*p)/ ((1-2*p)*33 + p*32*(1-(2*p)^5)):

Here's a numerical solution:

fsolve({eq1,eq2},{tau=0..1,p=0..1});
{p = 0.2897714582, tau = 0.03730507995}

I think a symbolic solution is unlikely.

Joe
 0
Joe
2/1/2005 5:52:54 AM
>> eqs:= {tau = 1 - (1-p)^(1/9),
>         tau = 2*(1-2*p)/ ((1-2*p)*33 + p*32*(1-(2*p)^5))};
>
>> fsolve(eqs,{tau=0..1,p=0..1});
>
>               {tau = 0.03730507995, p = 0.2897714582}
>
This is great!  Thanks very much!

Another question is, after the above two steps, I want to use these two
values of tau and p in my follow up codes.  But when I type

>p;
p
it seems Maple does not retain the variables in the first 2 steps.  I also
tried

> myp:=fsolve(eqs,{tau=0..1,p=0..1});
myp := {p = 0.2897714582, tau = 0.03730507995}
> myp[1];
p = 0.2897714582
> evalf(myp[1]);
p = 0.2897714582
> p;
p

I looked up in Maple's HELP but still got lost, even couldn't figure out in
which category this kind of problem lies.  Maple is powerful yet really
difficult to learn :-)

Xinhua
E&CE Dept.
Univ. Waterloo

 0
Xinhua
2/1/2005 3:33:19 PM
Xinhua Ling wrote:

> it seems Maple does not retain the variables in the first 2 steps.  I also
> tried
>
>
>>myp:=fsolve(eqs,{tau=0..1,p=0..1});
>
>          myp := {p = 0.2897714582, tau = 0.03730507995}

p and tau have not been assigned values after fsolve.

You could use
assign(myp);
after which p and tau are assigned the values above.

However, my preferred metod is
pt:=subs(myp, [p,tau]);
after which pt is a list of the two numbers found above. To get the
value for p (the first in the list) do
pt[1];
To get the value for tau do
pt[2];

Preben Alsholm
 0
Preben
2/1/2005 4:03:55 PM
In article <cto98k$uq8$1@news.net.uni-c.dk>,
Preben Alsholm  <P.K.Alsholm@mat.dtu.dk> wrote:

>However, my preferred metod is
>pt:=subs(myp, [p,tau]);
>after which pt is a list of the two numbers found above. To get the
>value for p (the first in the list) do
>pt[1];
>To get the value for tau do
>pt[2];

Or you could try

pt:= table(myp);

after which pt[p] and pt[tau] are the values of p and tau in this
solution.  This is especially useful in cases where there are
lots of variables and you don't want to have to remember what
order you put them in.

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

 0
israel
2/1/2005 10:46:14 PM
* Xinhua Ling writes:

> I looked up in Maple's HELP but still got lost, even couldn't figure out in
> which category this kind of problem lies.  Maple is powerful yet really
> difficult to learn :-)

> Thanks again for your help!

> Xinhua
> E&CE Dept.
> Univ. Waterloo
^^^^^^^^^^^^^^^^

This is what I would call "coming full circle".

SCNR

--
Space - the final frontier
 0
Oliver
2/2/2005 12:46:14 PM

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