import numpy as np import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = [12, 12] plt.rcParams.update({'font.size': 18}) n = 128 L = 30 dx = L/n x = np.arange(-L/2,L/2,dx,dtype='complex_') f = np.cos(x) * np.exp(-np.power(x,2)/25) # Function df = -(np.sin(x) * np.exp(-np.power(x,2)/25) + (2/25)*x*f) # Derivative
## Approximate derivative using finite difference dfFD = np.zeros(len(df),dtype='complex_') for kappa in range(len(df)-1): dfFD[kappa] = (f[kappa+1]-f[kappa])/dx dfFD[-1] = dfFD[-2]
## Derivative using FFT (spectral derivative) fhat = np.fft.fft(f) kappa = (2*np.pi/L)*np.arange(-n/2,n/2) kappa = np.fft.fftshift(kappa) # Re-order fft frequencies dfhat = kappa * fhat * (1j) dfFFT = np.real(np.fft.ifft(dfhat))
## Plots plt.plot(x,df.real,color='k',linewidth=2,label='True Derivative') plt.plot(x,dfFD.real,'--',color='b',linewidth=1.5,label='Finite Diff.') plt.plot(x,dfFFT.real,'--',color='r',linewidth=1.5,label='FFT Derivative') plt.legend() plt.show()
