Using fft and ifft with less frequencies than input points

I want to use fft and ifft in the context of heat equation. Therefore the grid needs to be refined, but I dont want to use as many coefficients in the fft:

%Grid
Nx = 10001;          
dx = L/(Nx-1);     
x = linspace(0,L,Nx)';

%Function
f = @(x) rectangularPulse(0.5, 1.5, x);
f_values = arrayfun(f,x);
u0 = ifft(fft(f_values)); %Takes very long

What I would want to do, is to insert an N, f.e. N=100, but get an array 10001x1.

Thanks.

Answer 1

[Matt J]

What I would want to do, is to insert an N, f.e. N=100, but get an array 10001x1.

%Grid
Nx = 100;  
L = 10;
dx = L/(Nx-1);     
x = linspace(0,L,Nx)';

%Function
f = @(x) rectangularPulse(0.5, 1.5, x);
f_values = arrayfun(f,x);
u0 = ifft(fft(f_values),10001);

whos u0

  Name          Size             Bytes  Class     Attributes

  u0        10001x1             160016  double    complex