Mathematics · Numerical Analysis
Consider the ordinary differential equation (ODE): y'(x) + y(x) = 0 for x > 0, with y(0) = 1. To solve this ODE, the following numerical scheme is used: Yn+1 - Yn-12h + Yn-1 = 0 for n ≥ 1, with Y0 = 1 and Y1 = 1. If 0 < h < 1/2, then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(Yn) → ∞ as n → ∞✓
- 2(Yn) → 0 as n → ∞
- 3(Yn) is bounded
- 4maxnh∈[0,T] |y(nh) - Yn| → ∞ as T → ∞
Correct answer
(Yn) → ∞ as n → ∞
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