diff_eq3.py

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