- #1
maistral
- 240
- 17
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?
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?