Allied & ICAR Exam Bank • ALLIED_1048 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical differentiation

Question Statement:

The central difference approximation for the second derivative $\frac{d^2 y}{dx^2}$ with step size $h$ has a truncation error of:

Options:

  • (A) O(h^2)
  • (B) O(h)
  • (C) O(h^3)
  • (D) O(h^4)

Answer Key:

A

Step-by-Step Solution & Explanation

Central difference formula: $y''(x) = \frac{y(x+h) - 2y(x) + y(x-h)}{h^2} + O(h^2)$. The leading error term is proportional to $h^2$.
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