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Diffstat (limited to 'odes.org')
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@@ -11,40 +11,36 @@ In this tutorial we shall look at solving Ordinary Differential Equations, ODE henceforth using odeint in Python. In this tutorial we shall be using - the concepts of arrays, functions and lists which we have covered in various + the concepts of arrays, functions and lists which we have covered in previous tutorials. Let's consider the classic problem of the spread of an epidemic in a population. This is given by the ordinary differential equation dy/dt = ky(L-y) where L is the total population and k is an arbitrary constant. For our - problem Let us use L=25000, k=0.00003. + problem Let us use L=250000, k=0.00003. Let the boundary condition be y(0)=250. Let's now fire up IPython by typing ipython -pylab interpreter. - As we saw in one of earlier session, sometimes pylab wont 'import' all - packages. For solving 'ordinary differential equations' also we shall - have to import 'odeint' function which is a part of the SciPy package. + As we saw in one of the earlier sessions, sometimes we will need more than + pylab to get our job done. For solving 'ordinary differential equations' + we shall have to import 'odeint' function, which is a part of the SciPy package. So we run the magic command: In []: from scipy.integrate import odeint - For now just remember this as a command that does some magic to obtain - the function odeint in to our program. The details regarding `import' shall be covered in a subsequent tutorial. We can represent the given ODE as a Python function. This function takes the dependent variable y and the independent variable t as arguments and returns the ODE. - Our function looks like this: - (Showing the slide should be sufficient) Let us now define our function. In []: def epid(y, t): .... k = 0.00003 - .... L = 25000 + .... L = 250000 .... return k*y*(L-y) Independent variable t can be assigned the values in the interval of @@ -118,13 +114,10 @@ In []: pend_sol = odeint(pend_int, initial,t) - In []: plot(pend_sol[0], t) plot theta against t - In []: plot(pend_sol[1], t) will plot omega against t - Plotting theta against t and omega against t we obtain the plots as shown - in the slide. + In []: plot(pend_sol) + This gives us 2 plots. The green plot is omega vs t and the blue is theta vs t. - Thus we come to the end of this tutorial on solving ordinary differential - equations in Python. In this tutorial we have learnt how to solve ordinary + Thus we come to the end of this tutorial. In this tutorial we have learnt how to solve ordinary differential equations of first and second order. *** Notes |