Graduate Spectral Theorem to Convert PDE into ODE

[mertcan]

Hi, in the link https://math.stackexchange.com/ques...ear-pde-by-an-ode-on-the-fourier-coefficients there is a nice example related to spectral theorem using Fourier series. Also in the link http://matematicas.uclm.es/cedya09/archive/textos/129_de-la-Hoz-Mendez-F.pdf you can see that in order to solve PDE using Exponential Time Differencing (ETD scheme) or Runge Kutta (RK) or ETDRK scheme conversion of PDE to ODE is required to use previous numerical methods. My question is : Can we always convert any kind of PDE into ODE using Fourier spectral theorem in order to employ Exponential Time Differencing (ETD scheme) or Runge Kutta (RK) or ETDRK numerical approximation method? I am asking because there are other methods for conversion but I wonder ALWAYS FOURIER SPECTRAL THEOREM works??

 

[mertcan]

My question is so simple : Can we always convert any kind of PDE into ODE using Fourier spectral theorem in order to employ Exponential Time Differencing (ETD scheme) or Runge Kutta (RK) or ETDRK numerical approximation method?

For more details or related links then you can see my post 1...

 

[mathwonk]

i do not know the answer but in view of the often stated opinion that ode is a standard base of theory and pde is not, i guess: no!