Use Euler with h = 0.5 for y′ = y − t² + 1, y(0) = 0.5. Find w₁.
Compare with the model answer
w₁ = 0.5 + 0.5·(0.5 − 0 + 1) = 1.25.
Euler's method wᵢ₊₁ = wᵢ + h f(tᵢ, wᵢ) and its error.
Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.
Euler: w₀ = α, wᵢ₊₁ = wᵢ + h·f(tᵢ, wᵢ). First order: global error O(h).
Use Euler with h = 0.5 for y′ = y − t² + 1, y(0) = 0.5. Find w₁.
w₁ = 0.5 + 0.5·(0.5 − 0 + 1) = 1.25.