| Topic: |
Science > Physics |
| User: |
"Mike" |
| Date: |
18 May 2007 02:01:15 AM |
| Object: |
How to solve the following differential equation? |
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
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| User: "Robert Israel" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 01:07:24 PM |
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"Mike" <meatheadIV@gmail.com> writes:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Symbolically or numerically? It's a separable DE, but the
integral won't have a closed form in general, even if r was
an integer > 1. Numerically, the usual methods should have
no trouble with it.
--
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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| User: "Peter Spellucci" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 09:35:48 AM |
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In article <f2jivp$296$1@news.Stanford.EDU>,
"Mike" <meatheadIV@gmail.com> writes:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
no numerical solution without initial value:
ask Maple, Mathematica or look here
Kamke: Differetialgleichungen ,
Loesungsmethoden und Loesungen
hth
peter
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| User: "Mike" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 12:26:42 PM |
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"Peter Spellucci" <spellucci@fb04373.mathematik.tu-darmstadt.de> wrote in
message news:f2kdk4$vi$1@fb04373.mathematik.tu-darmstadt.de...
In article <f2jivp$296$1@news.Stanford.EDU>,
"Mike" <meatheadIV@gmail.com> writes:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
no numerical solution without initial value:
ask Maple, Mathematica or look here
Kamke: Differetialgleichungen ,
Loesungsmethoden und Loesungen
hth
peter
Before numerical stuff, is it possible for closed-form solution? Thanks!
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| User: "Eric Gisse" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 02:46:16 AM |
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On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
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| User: "Bruce Scott TOK" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 09:42:38 AM |
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How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
All he needs is to learn how to do y log y via integration by parts
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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| User: "Mike" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 12:27:08 PM |
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"Bruce Scott TOK" <Use-Author-Supplied-Address-Header@[127.1]> wrote in
message news:200705181442.l4IEgcIL019059@ipp.mpg.de...
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
All he needs is to learn how to do y log y via integration by parts
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
How? Sorry I am a little bit rusty in these stuff... could you elaborate
more?
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| User: "Bruce Scott TOK" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 01:18:43 PM |
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Mike wrote:
"Bruce Scott TOK" <Use-Author-Supplied-Address-Header@[127.1]> wrote in
message news:200705181442.l4IEgcIL019059@ipp.mpg.de...
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
All he needs is to learn how to do y log y via integration by parts
How? Sorry I am a little bit rusty in these stuff... could you elaborate
more?
Actually, it looks perhaps easier to divide through by y and then
relabel x = log y, so that
x' = c1*x + c2 + c3 exp[ (r-1) x ] where x=x(t)
As the other poster says, you can set up the integral for t as a
function of x but that's as far as it goes analytically (i.e., "reduce
the problem to quadratures").
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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| User: "Peter Spellucci" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 01:11:27 PM |
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In article <200705181442.l4IEgcIL019059@ipp.mpg.de>,
Bruce Scott TOK <Use-Author-Supplied-Address-Header@[127.1]> writes:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
All he needs is to learn how to do y log y via integration by parts
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
???
int(1/(c1*y*log(y)+c2*y+c3*y^r) dy ) = ???
sorry
peter
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| User: "" |
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| Title: Re: How to solve the following differential equation? |
18 May 2007 02:34:47 PM |
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On May 18, 7:42 am, Bruce Scott TOK <Use-Author-Supplied-Address-
Header@[127.1]> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
All he needs is to learn how to do y log y via integration by parts
Is it easy to integrate 1/[y log y + a y + b y^r]? I don't think so,
at least not for general r.
R.G. Vickson
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
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| User: "The Ghost In The Machine" |
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| Title: Re: How to solve the following differential equation? |
20 May 2007 10:42:42 PM |
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In sci.physics, Eric Gisse
<jowr.pi@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76930@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account from http://www.teranews.com
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| User: "Mike" |
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| Title: Re: How to solve the following differential equation? |
21 May 2007 09:53:33 PM |
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"The Ghost In The Machine" <ewill@sirius.tg00suus7038.net> wrote in message
news:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr.pi@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76930@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account from http://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results have
NANs inside, what's the problem? And even if there is no NAN, to what degree
shall I trust the results? And is there a way to evaluate the precision and
accuracy of the solution?
.
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| User: "The Ghost In The Machine" |
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| Title: Re: How to solve the following differential equation? |
23 May 2007 12:44:11 AM |
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In sci.math, Mike
<meatheadIV@gmail.com>
wrote
on Mon, 21 May 2007 19:53:33 -0700
<f2tluv$pno$1@news.Stanford.EDU>:
"The Ghost In The Machine" <ewill@sirius.tg00suus7038.net> wrote in message
news:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr.pi@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76930@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account from http://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results have
NANs inside, what's the problem? And even if there is no NAN, to what degree
shall I trust the results? And is there a way to evaluate the precision and
accuracy of the solution?
Well NaN + x = NaN, NaN - x = NaN, NaN * x = NaN, and NaN / x = NaN, so
if one has a NaN one might as well redo the entire ball o' wax.
I'm not up on numerical stability, regrettably.
--
#191,
Linux. Because Windows' Blue Screen Of Death is just
way too frightening to novice users.
--
Posted via a free Usenet account from http://www.teranews.com
.
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| User: "Mike" |
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| Title: Re: How to solve the following differential equation? |
24 May 2007 02:04:44 PM |
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"The Ghost In The Machine" <ewill@sirius.tg00suus7038.net> wrote in message
news:bu0di4-kci.ln1@sirius.tg00suus7038.net...
In sci.math, Mike
<meatheadIV@gmail.com>
wrote
on Mon, 21 May 2007 19:53:33 -0700
<f2tluv$pno$1@news.Stanford.EDU>:
"The Ghost In The Machine" <ewill@sirius.tg00suus7038.net> wrote in
message
news:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr.pi@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76930@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account from http://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results
have
NANs inside, what's the problem? And even if there is no NAN, to what
degree
shall I trust the results? And is there a way to evaluate the precision
and
accuracy of the solution?
Well NaN + x = NaN, NaN - x = NaN, NaN * x = NaN, and NaN / x = NaN, so
if one has a NaN one might as well redo the entire ball o' wax.
I'm not up on numerical stability, regrettably.
--
#191,
Linux. Because Windows' Blue Screen Of Death is just
way too frightening to novice users.
--
Posted via a free Usenet account from http://www.teranews.com
\\
I just coudn't figure out why it has a divide by zero error at a certain
point in the ODE solvers...
.
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| User: "Peter Spellucci" |
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| Title: Re: How to solve the following differential equation? |
25 May 2007 08:12:09 AM |
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In article <f34njm$3tv$1@news.Stanford.EDU>,
"Mike" <meatheadIV@gmail.com> writes:
"The Ghost In The Machine" <ewill@sirius.tg00suus7038.net> wrote in message
news:bu0di4-kci.ln1@sirius.tg00suus7038.net...
In sci.math, Mike
<meatheadIV@gmail.com>
wrote
on Mon, 21 May 2007 19:53:33 -0700
<f2tluv$pno$1@news.Stanford.EDU>:
"The Ghost In The Machine" <ewill@sirius.tg00suus7038.net> wrote in
message
news:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr.pi@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76930@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account from http://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results
have
NANs inside, what's the problem? And even if there is no NAN, to what
degree
shall I trust the results? And is there a way to evaluate the precision
and
accuracy of the solution?
Well NaN + x = NaN, NaN - x = NaN, NaN * x = NaN, and NaN / x = NaN, so
if one has a NaN one might as well redo the entire ball o' wax.
I'm not up on numerical stability, regrettably.
--
#191,
Linux. Because Windows' Blue Screen Of Death is just
way too frightening to novice users.
--
Posted via a free Usenet account from http://www.teranews.com
\\
I just coudn't figure out why it has a divide by zero error at a certain
point in the ODE solvers...
even if your initial value problem has a solution which exists for all time,
nevertheless the discretization may lead you outside the domain, means
y_discrete <= 0
in that case y*log(y) and y^r might become complex (in the matalb normal
operation mode) or return NaN.
anyway, you should use the form
y' = c1*y*log(y)+c2*y+c3*y^r
now think about initial value 0<y0<1 , say y0=0.3 x0=0
c1=1, c2=0.5, c3=0.5, r=1.75
the solution seems to exist for all time, but going monotonically down
being almost zero for t>=2.5
(I did integrate this with radau5 from Hairer and Wanner)
look here : http://numawww.mathematik.tu-darmstadt.de:8081/
now, taking euler explicit your first step is
y1=0.3+h*(-.36119184129+0.5*0.3+0.5*0.3^1.75)=0.3+h*(-.1503878343)
so this brings you already down direction zero (of course you take not a step
h=2 !), but the joined effect of several such steps might well result in leaving
the doamin of definition. you can use the "event" option of matlabs ode
integrators in order to capture such a case and make a restart with
smaller tolerances which imply smaller steps
hth
peter
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| User: "Virgil" |
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| Title: Re: How to solve the following differential equation? |
25 May 2007 02:43:20 PM |
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On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
I still get dy/dx = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
.
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| User: "Peter Spellucci" |
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| Title: Re: How to solve the following differential equation? |
29 May 2007 11:23:56 AM |
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In article <virgil-3D2622.13432025052007@comcast.dca.giganews.com>,
Virgil <virgil@comcast.net> writes:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
!!!!!! y'=dy/dx
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
I still get dy/dx = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
this contradicts your original writing ! see above!
peter
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| User: "Eric Gisse" |
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| Title: Re: How to solve the following differential equation? |
21 May 2007 10:40:45 PM |
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On May 21, 7:53 pm, "Mike" <meathea...@gmail.com> wrote:
"The Ghost In The Machine" <e...@sirius.tg00suus7038.net> wrote in messagenews:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr...@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76...@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account fromhttp://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results have
NANs inside, what's the problem? And even if there is no NAN, to what degree
shall I trust the results? And is there a way to evaluate the precision and
accuracy of the solution?
Now would be a good time to consult the MATLAB help file on the
various ODE routines.
Why are you using ODExx on this ODE? It can be expressed as an
integral - quadrature methods are superior in this instance.
.
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| User: "Mike" |
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| Title: Re: How to solve the following differential equation? |
24 May 2007 12:57:08 AM |
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"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1179803891.545469.296740@y18g2000prd.googlegroups.com...
On May 21, 7:53 pm, "Mike" <meathea...@gmail.com> wrote:
"The Ghost In The Machine" <e...@sirius.tg00suus7038.net> wrote in
messagenews:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr...@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76...@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this
up!
--
Posted via a free Usenet account fromhttp://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results
have
NANs inside, what's the problem? And even if there is no NAN, to what
degree
shall I trust the results? And is there a way to evaluate the precision
and
accuracy of the solution?
Now would be a good time to consult the MATLAB help file on the
various ODE routines.
Why are you using ODExx on this ODE? It can be expressed as an
integral - quadrature methods are superior in this instance.
I thought ODE solvers are faster than numerical integral, could you tell me
how to solve it using the quadrature integral method? Your suggestion is new
to me... Thanks!
.
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| User: "Peter Spellucci" |
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| Title: Re: How to solve the following differential equation? |
24 May 2007 08:59:36 AM |
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In article <f339ev$o36$1@news.Stanford.EDU>,
"Mike" <meatheadIV@gmail.com> writes:
"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1179803891.545469.296740@y18g2000prd.googlegroups.com...
On May 21, 7:53 pm, "Mike" <meathea...@gmail.com> wrote:
"The Ghost In The Machine" <e...@sirius.tg00suus7038.net> wrote in
messagenews:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr...@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76...@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this
up!
--
Posted via a free Usenet account fromhttp://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results
have
NANs inside, what's the problem? And even if there is no NAN, to what
degree
shall I trust the results? And is there a way to evaluate the precision
and
accuracy of the solution?
Now would be a good time to consult the MATLAB help file on the
various ODE routines.
Why are you using ODExx on this ODE? It can be expressed as an
integral - quadrature methods are superior in this instance.
I thought ODE solvers are faster than numerical integral, could you tell me
how to solve it using the quadrature integral method? Your suggestion is new
to me... Thanks!
I showed you this already in my last answer to your questions: solve
for given x
integral{y0 to y } 1/(c1*eta*log(eta)+c2*eta+c3*exp(log(eta)*r)) d_eta = x-x0
that means you use separation of variables and solve for y as a function of x
pointwise: x given -> y=y(x) next x ....
this is indeed much slower than ode{xyz} provided you need large number of values
(x,y).
hth
peter
.
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| User: "Mike" |
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| Title: Re: How to solve the following differential equation? |
24 May 2007 02:03:48 PM |
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"Peter Spellucci" <spellucci@fb04373.mathematik.tu-darmstadt.de> wrote in
message news:f345o8$qge$1@fb04373.mathematik.tu-darmstadt.de...
In article <f339ev$o36$1@news.Stanford.EDU>,
"Mike" <meatheadIV@gmail.com> writes:
"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1179803891.545469.296740@y18g2000prd.googlegroups.com...
On May 21, 7:53 pm, "Mike" <meathea...@gmail.com> wrote:
"The Ghost In The Machine" <e...@sirius.tg00suus7038.net> wrote in
messagenews:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr...@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76...@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this
up!
--
Posted via a free Usenet account fromhttp://www.teranews.com
Thanks folks. Let's say I got some numerical results from using
Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the
results
have
NANs inside, what's the problem? And even if there is no NAN, to what
degree
shall I trust the results? And is there a way to evaluate the
precision
and
accuracy of the solution?
Now would be a good time to consult the MATLAB help file on the
various ODE routines.
Why are you using ODExx on this ODE? It can be expressed as an
integral - quadrature methods are superior in this instance.
I thought ODE solvers are faster than numerical integral, could you tell
me
how to solve it using the quadrature integral method? Your suggestion is
new
to me... Thanks!
I showed you this already in my last answer to your questions: solve
for given x
integral{y0 to y } 1/(c1*eta*log(eta)+c2*eta+c3*exp(log(eta)*r)) d_eta =
x-x0
that means you use separation of variables and solve for y as a function
of x
pointwise: x given -> y=y(x) next x ....
this is indeed much slower than ode{xyz} provided you need large number of
values
(x,y).
hth
peter
Thanks Peter!
Yes, I somehow had an impression that numerical integration is much slower
than ODE... I hope there are exceptions...
.
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| User: "Eric Gisse" |
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| Title: Re: How to solve the following differential equation? |
24 May 2007 02:07:56 AM |
|
|
On May 23, 10:57 pm, "Mike" <meathea...@gmail.com> wrote:
"Eric Gisse" <jowr...@gmail.com> wrote in message
news:1179803891.545469.296740@y18g2000prd.googlegroups.com...
On May 21, 7:53 pm, "Mike" <meathea...@gmail.com> wrote:
"The Ghost In The Machine" <e...@sirius.tg00suus7038.net> wrote in
messagenews:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr...@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76...@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this
up!
--
Posted via a free Usenet account fromhttp://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results
have
NANs inside, what's the problem? And even if there is no NAN, to what
degree
shall I trust the results? And is there a way to evaluate the precision
and
accuracy of the solution?
Now would be a good time to consult the MATLAB help file on the
various ODE routines.
Why are you using ODExx on this ODE? It can be expressed as an
integral - quadrature methods are superior in this instance.
I thought ODE solvers are faster than numerical integral, could you tell me
how to solve it using the quadrature integral method? Your suggestion is new
to me... Thanks!
I can't unless you know the values of the constants.
As far as the integral methods...now would be a good time to again,
consult MATLAB help.
.
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| User: "Eric Gisse" |
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| Title: Re: How to solve the following differential equation? |
21 May 2007 10:45:41 PM |
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|
On May 21, 7:53 pm, "Mike" <meathea...@gmail.com> wrote:
"The Ghost In The Machine" <e...@sirius.tg00suus7038.net> wrote in messagenews:i2h7i4-ml7.ln1@sirius.tg00suus7038.net...
In sci.physics, Eric Gisse
<jowr...@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76...@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
--
#191,
"640K ought to be enough for anybody."
- allegedly said by Bill Gates, 1981, but somebody had to make this up!
--
Posted via a free Usenet account fromhttp://www.teranews.com
Thanks folks. Let's say I got some numerical results from using Matlab's
ODE23 and ODE45, and it warns about "dividing by zero", and the results have
NANs inside, what's the problem? And even if there is no NAN, to what degree
shall I trust the results? And is there a way to evaluate the precision and
accuracy of the solution?
Now would be a good time to consult the MATLAB help file on the
various ODE routines.
Why are you using ODExx on this ODE? It can be expressed as an
integral - quadrature methods are superior in this instance.
.
|
|
|
|
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| User: "Virgil" |
|
| Title: Re: How to solve the following differential equation? |
21 May 2007 01:10:31 AM |
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|
In article <i2h7i4-ml7.ln1@sirius.tg00suus7038.net>,
The Ghost In The Machine <ewill@sirius.tg00suus7038.net> wrote:
In sci.physics, Eric Gisse
<jowr.pi@gmail.com>
wrote
on 18 May 2007 00:46:16 -0700
<1179474376.207533.76930@p77g2000hsh.googlegroups.com>:
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:
How to solve the following differential equation?
y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r
where c1, c2, c3 are constants... and r is a non-integer
Thanks!
That looks integrable to me.
Well, I get
dx/dy = 1/(c1*y*log(y) + c2*y + c3*exp(log(y)*r))
so it looks a bit messy to me. :-) Of course numerical
methods would work to some extent.
If it really were "dx/dy = ...", the integration would be trivial, but
it should be "dy/dx =...", which is quite different kettle of haddock.
.
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