\[ \begin{aligned} k_1 &= \text{RHS}(f^n, t^n) \\ k_2 &= \text{RHS}(f^n + \tfrac{1}{2} \Delta t \, k_1, t^n + \tfrac{1}{2} \Delta t) \\ k_3 &= \text{RHS}(f^n + \tfrac{1}{2} \Delta t \, k_2, t^n + \tfrac{1}{2} \Delta t) \\ k_4 &= \text{RHS}(f^n + \Delta t \, k_3, t^n + \Delta t) \\ f^{n+1} &= f^n + \frac{\Delta t}{6}(k_1 + 2k_2 + 2k_3 + k_4) \end{aligned} \]