Dwight Reid

This presentation outlines solving second order differential equations (ode) with python. The solution is obtained numerically using the python scipy ode engine (integrate module), the solution is therefore not in analytic form but the output is as if the analytic function was computed for each time step. The method is generally applicable to solving a higher order differential equation with python as well.
We will use a series RLC circuit as our ordinary differential equations example.

Slide Show

Code

# -*- coding: utf-8 -*-
from scipy import integrate
from pylab import * # for plotting commands

def rlc(A,t): 
    Vc,x=A 
    V = 1.0 #voltageSource
    R = 5.0
    L=100.0e-9 #100nH
    C = 1.0e-9 #1nF
    res=array([x,(V-Vc-(x*R*C))/(L*C)])
    return res

time = linspace(0.0,0.6e-6,1001)
vc,x = integrate.odeint(rlc,[0.0,0.0],time).T
i=1.0e-9*x
figure()
plot(time,vc)
xlabel('t')
ylabel('Vc')
show()

Differential Equations – Python

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