Part CCSIR NET June 2025fixing-h-and-letting-n-grow-is-not-the-convergence-statement-about-h

Fixing h and letting n grow is not the convergence statement about h

Consider the initial value problem (IVP) y′ + y = 0, y(0) = 1. Let $(y_{n})$ be the iterates of forward Euler method, applied to the IVP, with step size h where 0 < h < 1. Then which of the following statements are true?

A.The sequence $(y_{n})$ does NOT converge
B. $y_{n} \to 0$ as $n \to \infty$ ✓
C. $0 \leq y_{n} \leq 1$ for n = 0, 1, 2, …✓
D.|y(nh $) - y_{n}$ | → 0 as $n \to \infty$ ✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests numerical convergence.

See pricing

50 are analysed free — try those first.

The trap it tests

Numerical convergence

A scheme assumed to converge, or to converge at its advertised rate.

Drill statements like this

Related counterexample: A convergent method is stable for any step size

Fixing h and letting n grow is not the convergence statement about h

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