# Crude Fourier Series approximation for PDEs.

by maistral
Tags: approximation, crude, fourier, pdes, series
 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 Fourier-PDE solutions?
 P: 4,570 Hey maistral. With a fourier series, you need to project your function to the fourier space to get the co-effecients. 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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