Results 1 to 4 of 4

Math Help - [SOLVED] Partial Differential Equations: How to tell if a PDE is Hyperbolic, Elliptic

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    70

    [SOLVED] Partial Differential Equations: How to tell if a PDE is Hyperbolic, Elliptic

    Hey guys,

    I am a bit confused as to how to tell if an ordinary differential eqn. is hyperbolic, parabolic, when given a random pde. For example, I was looking at a book and it gave this example to determine the type:

    Uxx - 3Uxy = 0

    The book said to use det A = (a11*a22) - (a12)^2, where 11 = xx, 12 = xy, 22 = yy. I tried working it out using this method and I got 0-9 = -9, but the book gets -9/4??

    I know there is also another method, such as B^2 - 4AC =0, >0, <0. Then thing is, I don't have any clue as to how to extract the B, A, C from the above equation. How can I tell which is A, B, C??? Thanks for any and all help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by spearfish View Post
    Hey guys,

    I am a bit confused as to how to tell if an ordinary differential eqn. is hyperbolic, parabolic, when given a random pde. For example, I was looking at a book and it gave this example to determine the type:

    Uxx - 3Uxy = 0

    The book said to use det A = (a11*a22) - (a12)^2, where 11 = xx, 12 = xy, 22 = yy. I tried working it out using this method and I got 0-9 = -9, but the book gets -9/4??

    I know there is also another method, such as B^2 - 4AC =0, >0, <0. Then thing is, I don't have any clue as to how to extract the B, A, C from the above equation. How can I tell which is A, B, C??? Thanks for any and all help.
    Go back to your notes or text book and check what matrix A is in terms of the coefficients of the PDE (its not what you think).

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,373
    Thanks
    48
    Quote Originally Posted by spearfish View Post
    Hey guys,

    I am a bit confused as to how to tell if an ordinary differential eqn. is hyperbolic, parabolic, when given a random pde. For example, I was looking at a book and it gave this example to determine the type:

    Uxx - 3Uxy = 0

    The book said to use det A = (a11*a22) - (a12)^2, where 11 = xx, 12 = xy, 22 = yy. I tried working it out using this method and I got 0-9 = -9, but the book gets -9/4??

    I know there is also another method, such as B^2 - 4AC =0, >0, <0. Then thing is, I don't have any clue as to how to extract the B, A, C from the above equation. How can I tell which is A, B, C??? Thanks for any and all help.
    In general, a linear second order PDE is of the form

    A u_{xx} + B u_{xy} + C u_{yy} + \,\text{lower order terms}\; = 0

    If B^2 - 4AC > 0, then it's hyperbolic,
    If B^2 - 4AC = 0, then it's parabolic,
    If B^2 - 4AC < 0, then it's elliptlic.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2009
    Posts
    70
    Thanks Danny and CaptainBlack! This helps guide me in the right direction. I appreciate your time.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] finding hyperbolic equations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 29th 2010, 06:28 AM
  2. Partial Differential Equations
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: December 10th 2009, 01:28 PM
  3. hyperbolic partial differential equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: November 25th 2009, 09:00 AM
  4. Partial Differential Equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: September 2nd 2009, 04:58 PM
  5. partial differential equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 9th 2009, 05:56 AM

Search Tags


/mathhelpforum @mathhelpforum