For the standard fourth-order classical Runge-Kutta method (RK4) with step size $h$, the local truncation error per step and the global truncation error over a fixed integration interval $[a, b]$ are of order:

(A) Local error $O(h^5)$, Global error $O(h^4)$

(B) Local error $O(h^4)$, Global error $O(h^3)$

(C) Local error $O(h^4)$, Global error $O(h^5)$

(D) Local error $O(h^3)$, Global error $O(h^2)$

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Method Order:** RK4 is a fourth-order accurate scheme ($p = 4$). 2. **Stage 2: Local Truncation Error:** Single-step Taylor series remainder is $O(h^{4+1}) = O(h^5)$. 3. **Stage 3: Global Error Accumulation:** Cumulative error over $N \sim 1/h$ steps is $N \times O(h^5) = O(h^4)$. 4. **Stage 4: Selection:** Option A is correct.

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