Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 17B / i

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- Solution i

Solution

The local truncation error is the error made by one numerical step started from the exact solution:

τ_{n + 1} = y (t_{n + 1}) - y (t_{n}) - h ϕ (t_{n}, y (t_{n}), h) .

A one-step method has local order

p + 1

when

τ_{n + 1} = O (h^{p + 1})

uniformly for

t_{n}

in each fixed bounded time interval.

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