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