Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple partial differential equation

  1. May 1, 2012 #1
    Hello.

    I have equation:

    [tex]\frac{\partial T}{\partial t}-\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0[/tex]

    I calculated determinant:

    [tex]\Delta=(-\frac{1}{2})^2)-4\cdot 1 \cdot 0 \Rightarrow \sqrt{\Delta}=\frac{1}{2} \\ (\frac{dT}{dt})_{1}=-\frac{1}{4} \\ (\frac{dT}{dt})_{2}=\frac{1}{4}[/tex]

    next

    [tex]T=-\frac{1}{4}t+C_{1} \Rightarrow T+\frac{1}{4}t=C_{1} \\ T=\frac{1}{4}t+C_{2} \Rightarrow T-\frac{1}{4}t=C_{2}[/tex]

    I am add a new coefficients [tex]\eta[/tex] and [tex]\xi[/tex], then

    [tex]\xi=\frac{1}{4}t+T\\ \eta=-\frac{1}{4}t+T[/tex]

    Then I calculated matrix jacobian's =[tex]\frac{1}{2}[/tex]

    Good?

    I greet

    Post edited
     
    Last edited: May 2, 2012
  2. jcsd
  3. May 1, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I'm not all that clear on what you are doing but that first statement is obviously untrue.
    [tex]\Delta= (-\frac{1}{2})^2- 4\cdot 1 \cdot 0= \frac{1}{4}[/tex]
    so
    [tex]\sqrt{\Delta}= \frac{1}{2}[/tex]
    not [itex]\sqrt{2}[itex]

     
  4. May 2, 2012 #3
    Thanks,

    Of course, I made mistake in write. I would like solve partial differential equation but I dont have experience. I edited my post.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple partial differential equation
Loading...