Newsgroup sci.math.num-analysis 28826

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Gopinath Warrier (mece2gn@jeston.uh.edu) writes:
> Hello,
> 
> 	I need to integrate a nonlinear ODE of the form 
> 
> f1(x,y)*(y'') + f2(x,y)*(y')^2 + f3(x,y)*(y') + f4(x,y) = g    ---- (1);
> 
> where, f1,f2,f3,f4 are polynomials.  At x = 0, y' = 0.  To find y(0), I
> 
> substitute x= 0 in (1), but it so turns out that f1=f2=f3=0 and the (1) 
> 
> becomes a nonlinear equation which can be solved for y(0).  
> 
> Thus it turns out that the condition y'(0) = 0, is not needed to find y(0), so 
> 
> does this mean that the solution of the ODE is independent of y'(0) ?.
      In general the theorem of existence says that for every point
         x=a , y= y(a), y'= y'(a)
there is one and only one solution passing through it provided that a
Lipschitz condition is satisfied. Generally such sondition is satisfied,
but one has to go away from 'singular' points.
   You will need, of course, the value of y'(a) at point x=a. If a=0 is
a singularity then take a=0.000000001 which is very close to your a=0
and find the solution. Good luck.
--
Angel, secretary (male) of Universitas Americae (UNIAM).
     http://www.ncf.carleton.ca/~bp887

In article (Dans l'article) <57851i$nlh@mark.ucdavis.edu>,
psalzman@landau.ucdavis.edu (I hate grading almost as much as taking in
class exams) wrote (écrivait) :
> Dear All,
> 
> I would like some advice on how to handle complex numbers in ANSI C.  
> My knowledge of C stops at structs, but from what litle I know about 
> structures, it seems like that would be the most clear way of handling 
> complex numbers.
> 
> If I wanted to load an array with values of a complex exponential, would
> I want to build an array of structures?  I'm picturing the structs to
> consist of two floats, one for the real part and the other for the
> imaginary part of the number.  Arithmatic would be done via functions
> which operated on the two struct components. 
> 
> Like I said, my knowledge of stuctures is sketchy.  Is what I just said
> approximately correct?  Is there a better way of doing it in ANSI C?
> 
> Much thanks!
> 
> Peter
The best way to deal with complexes is to hack in C++ : you don't use
structs but classes, it's much more powerful. You can then create
'operands' and managing complexes like classic numbers. For example, you
can initialize two complexes. Then, it's possible to add, substract,
multiply, divide them, rise them to a power, and so on.
For more flexibility, you can define complexes as a 2x2 matrix.
For more infos, mail back to : .
I think I could send you C/C++ routines to manage complexes.
-- 
M.TIBOUCHI
>See you soon on the Global Village

geof wrote:
> 
> ILLEGAL SCAM!!
> 
> YOU WILL NEVER SEE A DOLLAR OF YOUR MONEY AGAIN!!!
> 
> READ WHY!
> 
> http://www.usps.gov/websites/depart/inspect/chainlet.htm
> 
> Chain letters are a form of gambling, and sending them through the mail
> or delivering them in person or by computer, violates Title 18, United
> States Code, Section 1302, the Postal Lottery Statute.
> 
> (A copy of this chain letter has been sent to this person's Internet
> provider and Cc'd to jccheezum@uspis.gov, The U.S. Postal Inspection
> Service, with a list of all names involved. Another copy of all names
> and addresses has been forwarded to a local branch of the Internal
> Revenue Service.)
> 
> A chain letter is a "get rich quick" scheme that promises that your mail
> box will soon be stuffed full of cash if you decide to participate.
> You're told you can make thousands of dollars every month if you follow
> the detailed instructions in the letter.
> 
> A typical chain letter includes names and addresses of several
> individuals whom you may or may not know. You are instructed to send a
> certain amount of money--usually $5--to the person at the top of the
> list, and then eliminate that name and add yours to the bottom. You are
> then instructed to mail copies of the letter to a few more individuals
> who will hopefully repeat the entire process. The letter promises that
> if they follow the same procedure, your name will gradually move to the
> top of the list and you'll receive money -- lots of it.
> 
> There's at least one problem with chain letters. They're illegal if they
> request money or other items of value and promise a substantial return
> to the participants. Chain letters are a form of gambling, and sending
> them through the mail (or delivering them in person or by computer, but
> mailing money to participate) violates Title 18, United States Code,
> Section 1302, the Postal Lottery Statute. (Chain letters that ask for
> items of minor value, like picture postcards or recipes, may be mailed,
> since such items are not things of value within the meaning of the law.)
> 
> Recently, high-tech chain letters have begun surfacing. They may be
> disseminated over the Internet, or may require the copying and mailing
> of computer disks rather than paper. Regardless of what technology is
> used to advance the scheme, if the mail is used at any step along the
> way, it is still illegal.
> 
> The main thing to remember is that a chain letter is simply a bad
> investment. You certainly won't get rich. You will receive little or no
> money. The few dollars you may get will probably not be as much as you
> spend making and mailing copies of the chain letter.
> 
> Chain letters don't work because the promise that all participants in a
> chain letter will be winners is mathematically impossible. Also, many
> people participate, but do not send money to the person at the top of
> the list. Some others create a chain letter that lists their name
> numerous times--in various forms with different addressee. So, in
> reality, all the money in a chain is going to one person.
> 
> Do not be fooled if the chain letter is used to sell inexpensive reports
> on credit, mail order sales, mailing lists, or other topics. The primary
> purpose is to take your money, not to sell information. "Selling" a
> product does not ensure legality. Be doubly suspicious if there's a
> claim that the U.S. Postal Service or U.S. Postal Inspection Service has
> declared the letter legal. This is said only to mislead you. Neither the
> Postal Service nor Postal Inspectors give prior approval to any chain
> letter.
> 
> Participating in a chain letter is a losing proposition. Turn over any
> chain letter you receive that asks for money or other items of value to
> your local postmaster or nearest Postal Inspector. Write on the mailing
> envelope of the letter or in a separate transmittal letter, "I received
> this in the mail and believe it may be illegal."
Even though I'm against chain-letters to, and know it's scams,
I really think it's more ugly that there are some people like
you, who dont have anything ells to do then interfear and 
playing "net-police".
If people wants to spend 5 bucks on those scam, it's their
own business; I really dont think that you write this because
you care about other people, but because you love to play
wise-guy, which you are deffently not!!! Are you jaloux
on those who maybe earn som money or what? You may
have a very sad life since you spend so much time to "turn
people in" to their internet-provider; havent it occour to
you that many providers are sick and tired of people like you
who allways claim and hope the werst for other people.
I know that many who do this scam, they even dont know
that it's illegal, but let them find out of it self, not
by a person who love to play "hero"
Get of the net and get a life, and learn about the
real life and laws for that matter.

My HP 48GX calculator uses the Runge-Kutta Fehlberg method to solve first
order ODE's. I would like to implement this method instead of the ordinary
4th order Runge-Kutta method as a general ODE solver for problems in
hydraulics. If anyone could e-mail me details of the algorithm and if
possible the Excel Visual Basic for Applications code, I would be most
grateful.
Ciao!
Filipe
filipe@iafrica.com

AngelEyes (bluhme@post3.tele.dk) wrote:
: geof wrote:
: > 
: > ILLEGAL SCAM!!
: > 
: > YOU WILL NEVER SEE A DOLLAR OF YOUR MONEY AGAIN!!!
: > 
: > READ WHY!
: > 
: > http://www.usps.gov/websites/depart/inspect/chainlet.htm
: > 
: > Chain letters are a form of gambling, and sending them through the mail
: > or delivering them in person or by computer, violates Title 18, United
: > States Code, Section 1302, the Postal Lottery Statute.
: > 
: > (A copy of this chain letter has been sent to this person's Internet
: > provider and Cc'd to jccheezum@uspis.gov, The U.S. Postal Inspection
: > Service, with a list of all names involved. Another copy of all names
: > and addresses has been forwarded to a local branch of the Internal
: > Revenue Service.)
: > 
: > A chain letter is a "get rich quick" scheme that promises that your mail
: > box will soon be stuffed full of cash if you decide to participate.
: > You're told you can make thousands of dollars every month if you follow
: > the detailed instructions in the letter.
: > 
: > A typical chain letter includes names and addresses of several
: > individuals whom you may or may not know. You are instructed to send a
: > certain amount of money--usually $5--to the person at the top of the
: > list, and then eliminate that name and add yours to the bottom. You are
: > then instructed to mail copies of the letter to a few more individuals
: > who will hopefully repeat the entire process. The letter promises that
: > if they follow the same procedure, your name will gradually move to the
: > top of the list and you'll receive money -- lots of it.
: > 
: > There's at least one problem with chain letters. They're illegal if they
: > request money or other items of value and promise a substantial return
: > to the participants. Chain letters are a form of gambling, and sending
: > them through the mail (or delivering them in person or by computer, but
: > mailing money to participate) violates Title 18, United States Code,
: > Section 1302, the Postal Lottery Statute. (Chain letters that ask for
: > items of minor value, like picture postcards or recipes, may be mailed,
: > since such items are not things of value within the meaning of the law.)
: > 
: > Recently, high-tech chain letters have begun surfacing. They may be
: > disseminated over the Internet, or may require the copying and mailing
: > of computer disks rather than paper. Regardless of what technology is
: > used to advance the scheme, if the mail is used at any step along the
: > way, it is still illegal.
: > 
: > The main thing to remember is that a chain letter is simply a bad
: > investment. You certainly won't get rich. You will receive little or no
: > money. The few dollars you may get will probably not be as much as you
: > spend making and mailing copies of the chain letter.
: > 
: > Chain letters don't work because the promise that all participants in a
: > chain letter will be winners is mathematically impossible. Also, many
: > people participate, but do not send money to the person at the top of
: > the list. Some others create a chain letter that lists their name
: > numerous times--in various forms with different addressee. So, in
: > reality, all the money in a chain is going to one person.
: > 
: > Do not be fooled if the chain letter is used to sell inexpensive reports
: > on credit, mail order sales, mailing lists, or other topics. The primary
: > purpose is to take your money, not to sell information. "Selling" a
: > product does not ensure legality. Be doubly suspicious if there's a
: > claim that the U.S. Postal Service or U.S. Postal Inspection Service has
: > declared the letter legal. This is said only to mislead you. Neither the
: > Postal Service nor Postal Inspectors give prior approval to any chain
: > letter.
: > 
: > Participating in a chain letter is a losing proposition. Turn over any
: > chain letter you receive that asks for money or other items of value to
: > your local postmaster or nearest Postal Inspector. Write on the mailing
: > envelope of the letter or in a separate transmittal letter, "I received
: > this in the mail and believe it may be illegal."
: 
: Even though I'm against chain-letters to, and know it's scams,
: I really think it's more ugly that there are some people like
: you, who dont have anything ells to do then interfear and 
: playing "net-police".
: If people wants to spend 5 bucks on those scam, it's their
: own business; I really dont think that you write this because
: you care about other people, but because you love to play
: wise-guy, which you are deffently not!!! Are you jaloux
: on those who maybe earn som money or what? You may
: have a very sad life since you spend so much time to "turn
: people in" to their internet-provider; havent it occour to
: you that many providers are sick and tired of people like you
: who allways claim and hope the werst for other people.
: 
: I know that many who do this scam, they even dont know
: that it's illegal, but let them find out of it self, not
: by a person who love to play "hero"
: 
: Get of the net and get a life, and learn about the
: real life and laws for that matter.
-- 
Jeremy Michael May     |----------------------------|        Whittington 313
Post Office Box 5047   |   *** HAVE A NICE DAY ***  |        (601)-925-3074  
Clinton MS  39058      |____________________________|   Home (601)-947-7980 

I am seeking for some references, books or software about curve fitting
of peaks by gaussian\lorentzian functions. 
In particular, I am interested in the determination of the guess
parameters for the iterative method of Chi^2 least-square minimization
(Levenberg-Marquardt).
 Another problem may be the estimation of errors. 
Answer by e-mail please, scd@gopher.chem.wayne.edu

In article <01bbda2b$0875b000$697a07c4@filipeh>, filipe@iafrica.com says...
>
>My HP 48GX calculator uses the Runge-Kutta Fehlberg method to solve first
>order ODE's. I would like to implement this method instead of the ordinary
>4th order Runge-Kutta method as a general ODE solver for problems in
>hydraulics. If anyone could e-mail me details of the algorithm and if
>possible the Excel Visual Basic for Applications code, I would be most
>grateful.
>
>Ciao!
>
>Filipe
>
>filipe@iafrica.com
	The Runge-Kutta-Fehlberg scheme can be found in almost all numerical 
analysis textbooks. Try any of the following;
1. "Numerical Recipies in C"
2. "Numerical Analysis" by Kincaid, D. and Cheney, W.
3. "Numerical Solution of Ordinary Differential Equations" by Lapidus, L and
	Seinfeld, J. H. -- This book also discusses a variety of other 	
	Runge-Kutta schemes.
	Good Luck !
Gopinath Warrier		
Dept. of Mech. Engr.
Univ. of Houston.
4800 Calhoun Rd
Houston, TX - 77204

I hate grading almost as much as taking in class exams (psalzman@landau.ucdavis.edu) wrote:
: Dear All,
: I would like some advice on how to handle complex numbers in ANSI C.  
: My knowledge of C stops at structs, but from what litle I know about 
: structures, it seems like that would be the most clear way of handling 
: complex numbers.
You might find something about this in the book, "Numerical
Recipies in C", which is on line at:
http://cfatab.harvard.edu/nr/nronline.html
No guarantees though -- I haven't looked in this book specifically
for complex number handling routines.
-- Wetboy

hi
I'm reading Fletcher's 2nd edition on Practical Methods of
Optimization and on page 21, in the middle of the page, he states
"...the exact minimizing value of alpha is required and cannot be
implemented in parctice in a finite number of operations. (Essentially
the nonlinear equation df/dalpha=0 must be solved.)"
He's refering to the linsearch subproblem
   Find alpha^k to minimize f(x^k + alpha*s^k) w/r to alpha.
The df/dalpha=0 is the directional derivative of f in the direction
specified by s^k, which is unit direction. Thus,
df
--      = |grad f| * cos(theta) = 0
dalpha
I don't understand why this is a non-linear equation. I thought that
if an equation was linear in the derivatives of f, then it was a
linear differential equation. df/dalpha = 0 looks pretty linear to me.
I'm confused.
thanks.

In article <57851i$nlh@mark.ucdavis.edu> I hate grading almost as much as
taking in class exams, psalzman@landau.ucdavis.edu writes:
>Dear All,
>
>I would like some advice on how to handle complex numbers in ANSI C.  
>My knowledge of C stops at structs, but from what litle I know about 
>structures, it seems like that would be the most clear way of handling 
>complex numbers.
>
>If I wanted to load an array with values of a complex exponential, would
>I want to build an array of structures?  I'm picturing the structs to
>consist of two floats, one for the real part and the other for the
>imaginary part of the number.  Arithmatic would be done via functions
>which operated on the two struct components. 
>
>Like I said, my knowledge of stuctures is sketchy.  Is what I just said
>approximately correct?  Is there a better way of doing it in ANSI C?
>
>Much thanks!
>
>Peter
>
Structs are how I have done this  in the past.  Usually I define the
types and function prototypes in a header file (like cplx.h) and
implement the routines in a separate translation unit (cplx.c).  
The data types look something like this:
typedef struct ct {
    double real;
    double imag;
} Complex_t, *Complex_ptr;
This defines two new types, Complex_t and Complex_ptr.  An object of type
Complex_t has two members, real and imag, both of which are double
precision floats.  An object of type Complex_ptr is a pointer to an
object of type Complex_t.
Objects would be declared as follows:
    Complex_t a, b; /* a and b are objects of type Complex_t */
    Complex_t arr[10]; /* arr is an array of objects of type Complex_t */
    Complex_ptr p; /* p is a pointer to an object of type Complex_t */
Assignments can either be done to the individual fields, like this:
    a.real = 0.0;
    a.imag = 1.0;
    arr[i].real = 1.0;
    arr[i].imag = -2.0;
    p = &b;
    p->real = 2.0;  /* same as (*p).real = 2.0 */
    p->imag = -3.0;
Or, you could write a function which assigned two doubles to a complex. 
Note that the function could return the complex value, or take the
complex number as an argument.
/* Method 1 */
Complex_t cplx_assign1 (double r, double i)
{
    Complex_t result;
    result.real = r;
    result.imag = i;
    return (result);
}
/* Method 2 */
void cplx_assign2 (Complex_ptr dst, double r, double i)
{
    dst->real = r;
    dst->imag = i;
}
...
    a = cplx_assign1 (1.0, 2.0);
    cplx_assign2 (&b;, 3.0, 4.0);
The implementation of add, subtract, multiply, divide, etc., would be
similar.
Complex_t cplx_add (Complex_t a, Complex_t b)
{
    Complex_t result;
    result.real  = a.real + b.real;
    result.imag = a.imag + b.imag;
    return result;
}
The rest I think you can figure out for yourself.  Hope this was useful.

Hi! :)
I am doing my thesis job.  It is based in the numerical solution of the
neutron transport equation using nodal analitycal methods.
My problem is that I have found information about finite element methods
using polinomyal approximations, and I want to find an approximation using
an aproximation like:
	psi(x,y) = aP00 + bP01 + cP10 + d exp(-sx/m) + e exp(-sy/m)
Where Pij(x,y) = Pi(x)Pj(y), 0<=i,j<=1 are the Legendre's polinomyals
      s,m are real constants.
I want to solve this problem first in order to solve the (x,y,t) problem.
I would like to know where I can find information about nodal analytical
methods, and the models Raviart-Thomas, bilinear, Hennart-del Valle.
If you can help me suggesting me references, or places in internet where
I could find information I will thank you very much.
You can write me in English, French and Spanish.
		Sincerely yours,
			Jose Francisco Marquez Flores
				jfmflores@spin.com.mx