1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

[PDE] Transforming Hard Equations into Easier Ones

  1. Feb 24, 2013 #1
    I have a PDE and I have to transform it into an easier one using a substitution:

    [itex]u_t=u_{xx}-\beta u[/itex]

    I am supposed to use the following substitution:

    [itex]u(x,t)=e^{-\beta t}w(x,t)[/itex]

    I am supposed to get something that looks like this:

    [itex]w_t=w_{xx}[/itex]

    Can someone show me the steps?
     
  2. jcsd
  3. Feb 24, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Here are the steps. Substitute the form ##u(x,t) = e^{-\beta t}w(x,t)## into all terms of the PDE and collect terms. That means you will need to compute ##u_t## and ##u_{xx}## using standard calculus differentiation rules.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted