Mathematics · Numerical Analysis
Consider the initial value problem (IVP) y' + y = 0, y(0) = 1. Let (yn) be the sequence of iterates obtained by applying the forward Euler method to this IVP with a constant step size h, where 0 < h < 1. Which of the following statements is true?
- 1|y(nh) - yn| → ∞ as n → ∞
- 2yn ≥ 1 for all n = 1, 2, 3, ...
- 3yn → 0 as n → ∞✓
- 4The sequence (yn) does not converge
Correct answer
yn → 0 as n → ∞
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