Temporal discretization Uniform sampling:(t,t h,t 2h,... Explicit Euler integration: f化+=fO+hf@=f0+haf阳 at 1.Numerically stability:a sufficiently small time step h. Implicit Euler integration: f(t+h)=f(t)+hλ·Lf(t+h) →(I-hn·L)f(t+h)=f(t)Temporal discretization • Uniform sampling: (𝑡,𝑡 + ℎ,𝑡 + 2ℎ, … ) • Explicit Euler integration: 𝒇 𝑡 + ℎ = 𝒇 𝑡 + ℎ 𝜕𝒇 𝑡 𝜕𝑡 = 𝒇 𝑡 + ℎ𝜆 ∙ 𝐿𝒇(𝑡) 1. Numerically stability: a sufficiently small time step ℎ. • Implicit Euler integration: 𝒇 𝑡 + ℎ = 𝒇 𝑡 + ℎ𝜆 ∙ 𝐿𝒇(𝑡 + ℎ) ⟺ 𝑰 − ℎ𝜆 ∙ 𝐿 𝒇 𝑡 + ℎ = 𝒇 𝑡