 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/ii/solution

For

f^{'} = Φ (x, f)

, the Backward Euler method uses the slope at the end of the step:

y_{i + 1} = y_{i} + h Φ (x_{i + 1}, y_{i + 1}) .

This generally requires solving an implicit equation for

y_{i + 1}

. For a derivative depending only on

x

, it reduces to

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

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