Crude Fourier Series approximation for PDEs.by maistral Tags: approximation, crude, fourier, pdes, series 

#1
Dec1712, 01:43 PM

P: 72

Is there a way to "crudely" approximate PDEs with Fourier series?
By saying crudely, I meant this way: Assuming I want a crude value for a differential equation using Taylor series; y' = x + y, y(0) = 1 i'd take a = 0 (since initially x = 0), y(a) = 1, y'(x) = x + y; y'(a) = 0 + 1 = 1 y"(x) = 1 + y'; y"(a) = 1 + 1 = 2 y'"(x) = 0 + y"(x); y"'(a) = 0 + 2 = 2 then y ~ 1 + x + 2/2! x^2 + 2/3! x^3. Or something similar to that. Does this crude method have an analog to FourierPDE solutions? 



#2
Dec1712, 08:01 PM

P: 4,570

Hey maistral.
With a fourier series, you need to project your function to the fourier space to get the coeffecients. So the question is, how do you get an appropriate function to project to the trig basis if it's not explicit (i.e. you don't have f(x) but a DE system that describes it)? 


Register to reply 
Related Discussions  
Solving PDEs using Fouries Series ???  Differential Equations  12  
PDEs and Fourier transforms  is this problem too difficult?  Differential Equations  3  
a question on orthogonality relating to fourier analysis and also solutions of PDES  Calculus & Beyond Homework  1  
Complex Fourier Series & Full Fourier Series  Calculus & Beyond Homework  5  
finite approximation of PDEs  Calculus & Beyond Homework  0 