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

[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

thanks in advance

 

[Mark44]

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.

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?

I have tried methods using convolutions but have had no success

thanks in advance

 

[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)

 

[Mark44]

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.

 

[LAZYANGEL]

You have u_x=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.