Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability / 5 / b / ii / Solution

Let $h=1/N$, $x_j=jh$, and let $y_j$ approximate $y(x_j)$. The forward Euler method gives the difference equationThis geometric sequence has solutionFor fixed $\lambda$, the limit as $N\to \infty$ is $2e^{-\lambda }$, as required by the exact solution.