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Crude Fourier Series approximation for PDEs. 
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#1
Dec1712, 01:43 PM

P: 78

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: 4,573

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)? 


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