Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 341 / 5 / b / 2

Table of contents
- Solution 2

Solution

The trapezoidal rule is

y_{n + 1} - y_{n} = \frac{h}{2} (f (y_{n}) + f (y_{n + 1})) .

Interchanging

y_{n}

and

y_{n + 1}

while replacing

h

by

- h

leaves the equation unchanged. Its backward step is therefore exactly its inverse, and

method 2 is time symmetric

.

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