Input: {$u_i^0$}, ${\mathcal{F}}_h$, $h$, N, tol, n Output: {$u_i^0$(k)} for k = 0, …, N 1:  Apply boundary conditions to $u_i^0$ 2:  for k = 0, 1, …, N − 1 do 3:    if scheme == "Euler" then 4:      for i = 1, …, M do 5:        $u_i^{k+1}=u_i^k+h{\mathcal{F}}_h(u_{i-1}^k,u_i^k,u_{i+1}^k)$; 6:      end for 7:    else if scheme == "RK4" then 8:      for i = 1, …, M do 9:        K1, K2, K3, K4 10:      end for 11:    else if scheme == "Centroid" then 12:      Initialize: $u_i^{k+1}$ ← $u_i^k$ for all i 13:      for n = 0, 1, 2, …, n do 14:        for i = 1, …, M do 15:          $u_i^{n+1, k+1}$ ← $u_i^k$ 16:        end for 17:        Apply boundary conditions to {u_i^(n + 1, k + 1)} 18:        if || $u_i^{n+1, k+1}$− $u_i^{n, k+1}$|| ≤ tol then 19:          break 20:        end if 21:      end for 22:      Set $u_i^{ k+1}$ ← $u_i^{n+1, k+1}$ for all i 23:    end if 24:    Apply boundary conditions to {$u_i^{ k+1}$)} 25: end for 26: return {$u_i^{ k}$}, (k = 0, …, N)