title: Solving system of nonlinear equations with Python, Euler's formula
body: <p>I am working on solving and analyzing a system of differential equations in Python. First did I solve it with help of scipy.integrate dopri5 and scopes Odeint. Which worked out fine. Then I tried to solve the equations with use of the Euler's method. The equations and code is as followed, </p>
  
  <pre><code>dj = -mu*(J**3 - (C - C0)*J - F)
  
  dc = J + C*F + a*J**2
  
  df = J*F - C
  
  
  
  T = 100
  dt = 0.001
  t = np.linspace(0, T, int(T/dt)+1)
  j = np.zeros(len(t))
  c = np.zeros(len(t))
  f = np.zeros(len(t))
  
  # Initial condition
  j[0] = 0.1
  c[0] = -0.5
  f[0] = 0.1
  
  a = 0.3025
  C0 = 0.5
  mu = 50
  
  for i in range(len(t)):
      j[i+1] = j[i] + (-mu * (j[i]**3 - (c[i] - C0)*j[i] - f[i]))*dt
      c[i+1] = c[i] + (j[i] + c[i] * f[i] + (a * j[i])**2)*dt
      f[i+1] = f[i] + (j[i] * f[i] - c[i])*dt
  </code></pre>
  
  <p>Is there any reason why the Euler's method should not work when both the other two are? </p>