Study Guide: Scientific software engineering for a simple ODE problem

$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\tp}{\thinspace .} $$

The problem class

Model problem: $ u'=-au $, $ u(0)=I $, for $ t\in (0,T] $.

Class Problem stores the physical parameters $ a $, $ I $, $ T $

May also offer other data, e.g., $ \uex(t)=Ie^{-at} $

Implementation:

from numpy import exp

class Problem:
    def __init__(self, I=1, a=1, T=10):
        self.T, self.I, self.a = I, float(a), T

    def u_exact(self, t):
        I, a = self.I, self.a     # extract local variables
        return I*exp(-a*t)

Basic usage:

problem = Problem(T=5)
problem.T = 8
problem.dt = 1.5