Numerical Methods

In the classical fourth-order Runge–Kutta (RK4) method for solving $\frac{dy}{dx} = f(x, y)$ with step size $h$, the formula for the third intermediate slope $k_3$ is:

Options:

• (A) $h f\left(x_n + \frac{h}{2}, y_n + \frac{k_2}{2}\right)$
• (B) $h f\left(x_n + \frac{h}{2}, y_n + \frac{k_1}{2}\right)$
• (C) $h f(x_n + h, y_n + k_2)$
• (D) $h f\left(x_n + h, y_n + \frac{k_2}{2}\right)$