Allied & ICAR Exam Bank • ALLIED_0805 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

The classical 4th-order Runge-Kutta method (RK4) for solving first-order ODEs has a local truncation error of order:

Options:

  • (A) $O(h^5)$ and global truncation error $O(h^4)$
  • (B) $O(h^4)$ and global error $O(h^3)$
  • (C) $O(h^2)$
  • (D) $O(h)$

Answer Key:

A

Step-by-Step Solution & Explanation

RK4 has local truncation error of order $O(h^5)$, which accumulates over $N \sim 1/h$ steps to give a global truncation error of $O(h^4)$.
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