Using this approximation, we can iterate through the time steps and compute the value of U i at each time step. For example, starting at time step i and using the approximation above, we can compute the value of U i at time step i + 1 : U i + 1 = U i + Δ Δ t ⋅ ⋅ ( − − 1 ρ ρ ∑ ∑ j = 1 N ( ∂ ∂ p ∂ ∂ x ) j ∫ ∫ Ω Ω ϕ ϕ j ∂ ∂ ϕ ϕ i ∂ ∂ x d Ω Ω + ν ν ∑ ∑ j = 1 N ∫ ∫ Ω Ω ( ∂ ∂ 2 u ∂ ∂ x 2 ) j ϕ ϕ j ∂ ∂ 2 ϕ ϕ i ∂ ∂ x 2 d Ω Ω + ∫ ∫ Ω Ω f x ϕ ϕ i d Ω Ω )