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I Solving u_x=(sin(x))*(u) in Fourier space

  1. Jun 20, 2016 #1
    Does anyone know if it is possible to solve an equation of the type
    u_x=(sin(x))*(u)
    on a periodic domain using the fft.

    I have tried methods using convolutions but have had no success

    thanks in advance
     
  2. jcsd
  3. Jun 20, 2016 #2

    Mark44

    Staff: Mentor

    What does u_x mean in the context of your problem? It could possibly mean the partial derivative of u with respect to x, or it could mean the x-component of a vector u.

    Also, what are you trying to solve for?
     
  4. Jun 20, 2016 #3
    sorry, should have been more clear. u_x is the partial derivative of u w.r.t. x and i am trying to solve for u,

    du/dx=(sin(x))*(u)
     
  5. Jun 21, 2016 #4

    Mark44

    Staff: Mentor

    Is u a function of any variables other than x? If so, your equation is an ordinary differential equation, and one that is separable and easy to solve analytically.
     
  6. Jun 21, 2016 #5
    You have ux=sin(x)*u

    Can't you rewrite it as: y'=y*sin(x)? Solve it as ODE and instead of writing the constant, just assume it's a function of the other variables.
     
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