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Part BCSIR NET June 2024explicit-scheme-uses-the-left-endpoint

Explicit scheme uses the left endpoint

If the value of the approximate solution of the initial value problem y′(x)=x(y(x)+1),x∈R,y(0)=βy'(x) = x(y(x) + 1), x \in \mathbb{R}, y(0) = \beta at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β\beta is

  1. A.0
  2. B.−1
  3. C.2
  4. D.1✓ 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.

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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.

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