 Solution

ID: 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})

y_{j + 1} = y_{j} + h (- λ y_{j}) = (1 - \frac{λ}{N}) y_{j}, y_{0} = 2.

y_{j} = 2 (1 - \frac{λ}{N})^{j} (0 \leq j \leq N), y_{N} = 2 (1 - \frac{λ}{N})^{N} .

For fixed

λ

N \to \infty

2 e^{- λ}

, as required by the exact solution.

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