# import some packages
from __future__ import print_function
import numpy as np

########################
# define some functions:
########################

# RHS of $\partial_t u$
def set_rhs(u, rhs, t):
    rhs[0] = 2.0 
    rhs[1] = u[1]
    rhs[2] = 2.0*t
    return rhs

# u(t+dt) = u(t) + rhs * dt
def calc_unew(u, rhs, dt):
    return u + rhs * dt

# print columns with data at time t
def pr_data(t, u):
    print(t, end="  ")
    for i in range(0, len(u)):
        print(u[i], end="  ")
    print()


###############
# main program:
###############

# time step
dt = 0.001

# make evo vec. u and its rhs
N = 3
u = np.empty([N])  
rhs = np.empty([N])

# initial vals
t = 0.0
u[0] = 0.0
u[1] = 1.0
u[2] = 0.0

pr_data(t, u)

timesteps = 1000

# loop over time steps, and print results
for n in range(0, timesteps):
    # make time step, using simple Euler method
    t = t + dt
    set_rhs(u, rhs, t)
    u = calc_unew(u, rhs, dt)
    # print columns with data
    pr_data(t, u)