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

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1. Jun 20, 2016

vector_problems

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

2. Jun 20, 2016

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?

3. Jun 20, 2016

vector_problems

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)

4. Jun 21, 2016

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.

5. Jun 21, 2016

LAZYANGEL

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.