My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 6th, 2016, 11:27 PM   #1
Newbie
 
Joined: Feb 2016
From: israel

Posts: 17
Thanks: 3

ODE system

Hi guys,

I need some help solving the next ODE system:

w'+2*U*sin(psi)=0
wv'+2UV*sin(psi)=V''
WU'+(U^2-V^2)*sin(psi)=mTsin(psi)+U''

m,T,psi are constants

BCE's: U=V=W=0 @ x=0, U-->0 as x-->infinity, V-->(-1) as x-->infinity

Some guidance would be greatly appreciated.

shai

Last edited by skipjack; February 7th, 2016 at 02:55 PM.
shai is offline  
 
February 7th, 2016, 06:21 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

You appear to have three equations in four unknown functions, y, U, V, and W (I am assuming the "w" in the first two equations was intended to be "W"). You aren't going to be able to solve three equations for four unknowns.
Country Boy is offline  
February 7th, 2016, 01:31 PM   #3
Global Moderator
 
Joined: May 2007

Posts: 6,807
Thanks: 717

Quote:
Originally Posted by Country Boy View Post
You appear to have three equations in four unknown functions, y, U, V, and W (I am assuming the "w" in the first two equations was intended to be "W"). You aren't going to be able to solve three equations for four unknowns.
I see U,V, and W, but no y. It looks like 3 equations in 3 unknowns.
mathman is offline  
February 7th, 2016, 02:55 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 20,935
Thanks: 2209

I would guess that "v" and "w" should have been "V" and "W" respectively.

Where did the problem come from?
skipjack is offline  
February 8th, 2016, 04:16 AM   #5
Newbie
 
Joined: Feb 2016
From: israel

Posts: 17
Thanks: 3

My mistake, I only have u,v, and w (no y).
This problem comes from boundary layer theory (fluid dynamics).
The equations describe the flow over a spinning cone (similarity analysis of the Navier-Stokes equations).

I'm going to try and solve it with Maple numerically...

Last edited by skipjack; February 8th, 2016 at 05:33 AM.
shai is offline  
February 8th, 2016, 09:11 AM   #6
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Sorry! There was a bit of dirt on my screen that made a "v" look like a "y".
Country Boy is offline  
February 9th, 2016, 06:03 PM   #7
Senior Member
 
Joined: Feb 2016
From: Australia

Posts: 1,834
Thanks: 650

Math Focus: Yet to find out.
Have you tried solving it using Laplace Transform?

I had a bit of a try but am a bit rusty, and it was getting messy pretty quick. Plus, I have no idea whether it would be a suitable method.

Also, for the sakes of readability...

$\displaystyle W' + 2U\sin(\psi) = 0$
$\displaystyle WV' + 2UV\sin(\psi) = V''$
$\displaystyle WU' + (U^2 - V^2) \sin(\psi) = mT\sin(\psi) + U''$

Last edited by skipjack; February 9th, 2016 at 11:34 PM.
Joppy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
ode, system



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
To find a system of coordinates for visualise a system of equations Jhenrique Geometry 1 August 29th, 2015 06:33 AM
A system Dacu Calculus 7 July 1st, 2014 12:06 PM
system consigliere- Algebra 2 April 13th, 2013 09:47 AM
System MIDI Elementary Math 7 October 24th, 2010 07:53 AM
Difference between Metric System & International System? zain Elementary Math 1 April 7th, 2008 02:23 PM





Copyright © 2019 My Math Forum. All rights reserved.