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!

Heat equation and Wave equation problems

  1. Oct 25, 2012 #1
    1.
    Solve the Heat equation u_t = ku_xx for 0 < x < ∏, t > 0 with the initial condition

    u(x, 0) = 1 + 2sinx

    and the boundary conditions u(0, t) = u(∏, t) = 1

    (Notice that the boundary condition is not homogeneous)

    3.
    Find the solution of the Wave equation u_tt = 4 u_xx with

    u(0, t) = u (π/2, t) = 0, t > 0

    u(x, 0) = sin (2x) - 2sin(6x), u_x (x, 0) = -3 sin4x, 0 ≤ x ≤ ∏/2

    Please help!! =[....
     
  2. jcsd
  3. Oct 26, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi dominic.tsy! welcome to pf! :smile:

    (try using the X2 button just above the Reply box :wink:)

    show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Oct 26, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Define v(x, t)= u(x,t)- 1. What differential equation, boundary condition, and initial condition does that satisfy?

    Try a Fourier series solution of the form [tex]\sum A_n(t) sin(nx/4)+ B)n(t)cos(nx/4)[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Heat equation and Wave equation problems
  1. Heat Equation Problem (Replies: 2)

Loading...