finite_difference/src/trunc/trunc_decay_FE.py

"""
Empirical estimation of the truncation error in a scheme.
Examples on the Forward Euler scheme for the decay ODE u'=-au.
"""
import numpy as np
import trunc_empir

def decay_FE(dt, N):
    dt = float(dt)
    t = np.linspace(0, N*dt, N+1)
    u_e = I*np.exp(-a*t)  # exact solution, I and a are global
    u = u_e  # naming convention when writing up the scheme
    R = np.zeros(N)

    for n in range(0, N):
        R[n] = (u[n+1] - u[n])/dt + a*u[n]

    # Theoretical expression for the trunction error
    R_a = 0.5*I*(-a)**2*np.exp(-a*t)*dt

    return R, t[:-1], R_a[:-1]

if __name__ == '__main__':
    I = 1; a = 2  # global variables needed in decay_FE
    trunc_empir.estimate(decay_FE, T=2.5, N_0=6, m=4, makeplot=True)