19.3 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:

.

The solution to this problem is a function . A numerical method computes approximations,  at discrete  communications points, , within the interval of interest . 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
        """
        self.rhs...