In the classical fourth-order Runge–Kutta (RK4) method for solving first-order ODEs with step size $h$, the local truncation error per step is of order:
Options:
(A) $O(h)$
(B) $O(h^3)$
(C) $O(h^4)$
(D) $O(h^5)$
Answer Key:
D
Step-by-Step Solution & Explanation
In the Runge–Kutta 4th order method, the Taylor series expansion matches up to $h^4$. Therefore, the local truncation error (error committed in a single step) is $O(h^5)$. The global truncation error (accumulated error over $N = (b-a)/h$ steps) is $O(h^4)$.