 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-2/17b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

y^{'} = λ y .

If one step has the form

y_{n + 1} = R (z) y_{n}, z = hλ,

then

R

S = {z \in C : ∣ R (z) ∣ \leq 1} .

The method is A-stable when

{z : Re z \leq 0} \subseteq S,

so it does not amplify any mode that the exact differential equation does not amplify.

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