CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Solving a nonlinear equation?

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   February 16, 2004, 10:22
Default Solving a nonlinear equation?
  #1
Pr
Guest
 
Posts: n/a
I need to solve such a problem cos(wa)cos(wb)-sin(wa)sin(wb)[1+ne^(iw\tau)]=0 where a,b,n and \tau are given values.The following equations is to be solved for w whereas i=\sqrt(-1). Please provide some suggestions are some reference to solve it
  Reply With Quote

Old   February 18, 2004, 05:38
Default Re: Solving a nonlinear equation?
  #2
Pr
Guest
 
Posts: n/a
Just the number of visits or increasing but nobody tried to answer it. Is it too difficult or too simple to answer it. Come on somebody atleast give me some references. Pr
  Reply With Quote

Old   February 18, 2004, 10:11
Default Re: Solving a nonlinear equation?
  #3
ag
Guest
 
Posts: n/a
Do you want an exact solution or an approximate solution? Numerically I would use a Newton-based iterative method, which can be found in any decent testbook covering numerical methods.
  Reply With Quote

Old   February 18, 2004, 10:13
Default Re: Solving a nonlinear equation?
  #4
Linfeng
Guest
 
Posts: n/a
Try Maple or Mathematica, if you are not writing a code

Linfeng
  Reply With Quote

Old   February 18, 2004, 11:33
Default Re: Solving a nonlinear equation?
  #5
Pr
Guest
 
Posts: n/a
yes thanks for the answers atleast. But there is a problem that it involves imaginary number(i).Then how do you solve such a problem. I know the numerical methods and know how to use a matlab when I have real numbers but this equation involves imaginary number that is why I am asking. Pr
  Reply With Quote

Old   February 18, 2004, 11:54
Default Re: Solving a nonlinear equation?
  #6
m malik
Guest
 
Posts: n/a
Do you have some sample numbers a, b, n, and tau, and the solution w?
  Reply With Quote

Old   February 18, 2004, 12:03
Default Re: Solving a nonlinear equation?
  #7
Pr
Guest
 
Posts: n/a
Yes I have but the methods should be applied in general to any value. Pr
  Reply With Quote

Old   February 18, 2004, 12:22
Default Re: Solving a nonlinear equation?
  #8
Tom
Guest
 
Posts: n/a
Since you're function is analytic (in the complex plane sense) you can use Newton-Raphson exactly as you would for a real number - in fortran change REAL w to COMPLEX w.

Alternatively split into real and imaginary parts and apply Newton iteration to the system.

Tom.
  Reply With Quote

Old   February 19, 2004, 04:21
Default Re: Solving a nonlinear equation?
  #9
ZZ
Guest
 
Posts: n/a
Use an equality: exp(I*w*tau)=cos(w*tau) + I*sin(w*tau), where I=sqrt(-1), and then you have two real equations.
  Reply With Quote

Old   February 19, 2004, 05:16
Default Re: Solving a nonlinear equation?
  #10
Pr
Guest
 
Posts: n/a
Hi ZZ do you mean by this cos(wa)cos(wb)-sin(wa)sin(wb)[1+ne^(iw\tau)]=0 cos(wa)cos(wb)-sin(wa)sin(wb)[1+n(cos(w\tau)+isin(w\tau)]=0 it is in this form

A*B-C*D[1+x+iy]=0

A*B-C*D*x-C*D*y*i=0

A*B-C*D*x=0----(1) C*D*y=0----(2) Pr
  Reply With Quote

Old   February 19, 2004, 05:54
Default Re: Solving a nonlinear equation?
  #11
Tom
Guest
 
Posts: n/a
Since w will in general be complex you can't do it that way. If w is real you can obtain two equations this way - the first equation will give you an infinite set of possible values of w while the second is a constraint upon your constants which needs to be satisfied in order that you have a solution - for arbitrary choices of your constant there will not be a real solution for w.
  Reply With Quote

Old   February 22, 2004, 06:50
Default flow separation
  #12
yousef
Guest
 
Posts: n/a
i ask if i have a poasitive pressure graident that must i have flow separation and thanks pleasese contact me at my email yelhasdi@yahoo.com
  Reply With Quote

Old   February 22, 2004, 10:17
Default Re: Solving a nonlinear equation?
  #13
CFD Learner
Guest
 
Posts: n/a
r u sure MATLAB could not handle imaginary problems?????
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Moving mesh Niklas Wikstrom (Wikstrom) OpenFOAM Running, Solving & CFD 122 June 15, 2014 06:20
Orifice Plate with a fully developed flow - Problems with convergence jonmec OpenFOAM Running, Solving & CFD 3 July 28, 2011 05:24
Differences between serial and parallel runs carsten OpenFOAM Bugs 11 September 12, 2008 11:16
IcoFoam parallel woes msrinath80 OpenFOAM Running, Solving & CFD 9 July 22, 2007 02:58
Could anybody help me see this error and give help liugx212 OpenFOAM Running, Solving & CFD 3 January 4, 2006 19:07


All times are GMT -4. The time now is 16:31.