Question

The final corrector of the fourth-order Runge-Kutta method uses ___________

(a) Midpoint rule

(b) Backward Euler method

(c) Simpson’s rule

(d) Trapezoidal rule

I got this question in semester exam.

This intriguing question originated from Transient Flows in section Transient Flows of Computational Fluid Dynamics

Answer 1

The correct answer is (c) Simpson’s rule

Explanation: The third step of the fourth-order Runge-Kutta method uses midpoint rule to correct the values and the last step uses Simpson’s rule. This renders a fourth-order accuracy to the Runge-Kutta method.