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 and end time
        name descriptive name of the problem...