Question Bank • QB_EM_167 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

The standard fourth-order Runge-Kutta (RK4) method for solving initial value problems has a local truncation error of order:

Options:

  • (A) $\mathcal{O}(h^5)$
  • (B) $\mathcal{O}(h^4)$
  • (C) $\mathcal{O}(h^3)$
  • (D) $\mathcal{O}(h^2)$

Answer Key:

A

Step-by-Step Solution & Explanation

For the classical RK4 method, the local truncation error per step is $\mathcal{O}(h^5)$, which accumulates to a global truncation error of $\mathcal{O}(h^4)$ over a finite interval.
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