 Solution

ID: past-exam-of-the-numerical-analysis-course-of-the-university-of-oxford/2021/3/c/i/solution

No. A necessary condition for consistency of a numerical method is reproduction of the constant solution

y (x) = 1

y^{'} = 0

ρ (1) = \sum_{j = 0}^{k} α_{j} = 0.

But the reverse triangle inequality gives, under the strict coefficient inequality,

∣ ρ (1) ∣ \geq ∣ α_{k} ∣ - j = 0 \sum k - 1 ∣ α_{j} ∣ > 0.

Thus the necessary order conditions for a linear multistep method already fail at order zero, regardless of the values of the

β_{j}

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