import numpy as np

class ForwardEuler_v1(object):

def __init__(self, f, U0, T, n):

self.f, self.U0, self.T, self.n = f, dt, U0, T, n

self.dt = T/float(n)

self.u = np.zeros(n+1)

self.t = np.zeros(n+1)

def solve(self):

"""Compute solution for 0 <= t <= T."""

self.u[0] = float(self.U0)

self.t[0] = float(0)

for k in range(self.n):

self.k = k

self.t[k+1] = self.t[k] + self.dt

self.u[k+1] = self.advance()

return self.u, self.t

def advance(self):

"""Advance the solution one time step."""

u, dt, f, k, t = \

self.u, self.dt, self.f, self.k, self.t

u_new = u[k] + dt*f(u[k], t[k])

return u_new