Study Guide: Scientific software engineering for a simple ODE problem

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

Test of wrong use

Find input data that may cause trouble and test such cases

Here: the formula for $ u^{n+1} $ may involve integer division

Example:

theta = 1; a = 1; I = 1; dt = 2

may lead to integer division:

(1 - (1-theta)*a*dt)  # becomes 1
(1 + theta*dt*a)      # becomes 2
(1 - (1-theta)*a*dt)/(1 + theta*dt*a)  # becomes 0 (!)

Test that solver does not suffer from such integer division:

def test_potential_integer_division():
    """Choose variables that can trigger integer division."""
    theta = 1; a = 1; I = 1; dt = 2
    N = 4
    u, t = decay_mod.solver(I=I, a=a, T=N*dt, dt=dt, theta=theta)
    u_de = np.array([exact_discrete_solution(n, I, a, theta, dt)
                     for n in range(N+1)])
    diff = np.abs(u_de - u).max()
    nt.assert_almost_equal(diff, 0, delta=1E-14)