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
Euler's method wᵢ₊₁ = wᵢ + h f(tᵢ, wᵢ) and its error.
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Formula
Notes
Euler: w₀ = α, wᵢ₊₁ = wᵢ + h·f(tᵢ, wᵢ). First order: global error O(h).
Exam angle
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