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

Splitting PDE into system of PDEs

  1. Jul 14, 2010 #1
    Hello:

    I am wondering if there is a general way of splitting the following PDE into two separate equations. I would like to re-write the second-order spatial derivatives on the LHS as first-order derivatives.

    [tex]
    \[
    \frac{{\partial p^2 }}{{\partial x^2 }} + \frac{{\partial p^2 }}{{\partial y^2 }} = A\frac{{\partial ^2 p}}{{\partial t^2 }} + B\frac{{\partial p}}{{\partial t}}
    \]
    [/tex]

    So once the above equation is split, there should be two equations involving only first-order spatial derivatives ([tex]\partial p/\partial x[/tex] and [tex]\partial p/\partial y[/tex]).
     
  2. jcsd
  3. Jul 15, 2010 #2
    I think that this equation can be split using the following rules:

    (1) The LHS of the wave equation is split by introducing another variable and removing a del operator.

    [tex]
    \[
    \frac{{\partial \psi }}{{\partial t}} = \nabla p
    \]
    [/tex]


    (2) The RHS of the wave equation is split by removing a derivative:

    [tex]
    \[
    \nabla \psi = A\frac{{\partial p}}{{\partial t}} + Bp
    \]
    [/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook