The <trapezoidal rule> is
$$
y_{n+1}-y_n=\frac h2(f(y_n)+f(y_{n+1})).
$$
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 $\boxed{\text{method 2 is time symmetric}}$.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-341/5/b/2/solution