Solving initial value problems

In this section, we will consider the mathematical task of numerically solving a system of ordinary equations for given initial values:

y'(t) = f(t, y)      y(t₀) = y₀∈ ℝⁿ

The solution of this problem is a function y. A numerical method aims at computing good approximations, y_i≈ y(t_i) at discrete points, the communications points t_i, within the interval of interest [t₀, t_e]. We collect the data that describes the problem in a class, as follows:

class IV_Problem:
    """
    Initial value problem (IVP) class
    """
    def __init__(self, rhs, y0, interval, name='IVP'):
        """
        rhs 'right hand side' function of the ordinary differential
                                                   equation f(t,y)
        y0 array with initial values
        interval start and end value of the interval of independent
        variables often initial...