 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/6/d/i/solution

f^{'} (x) = Φ (x, f (x))

y_{0}

. The forward Euler method uses the slope at the start of the step:

y_{i + 1} = y_{i} + h Φ (x_{i}, y_{i}), 0 \leq i < n .

If the derivative is a known function of

x

alone, this is

y_{i + 1} = y_{i} + h f^{'} (x_{i})

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