Skip to content
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 (yn)(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?

  1. A.The sequence (yn)(y_{n}) does NOT converge
  2. B.yn→0y_{n} \to 0 as n→∞n \to \infty✓ Correct
  3. C.0≤yn≤10 \le y_{n} \le 1 for n = 0, 1, 2, …✓ Correct
  4. D.|y(nh)−yn) - y_{n}| → 0 as n→∞n \to \infty✓ Correct

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

More on this topic

The chapter behind this: Numerical methods for ODE — free to read

From Numerical Analysis › Numerical ODE: Euler, Runge–Kutta

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram