Question

Which of these formulae is used for the corrector step of the two-level predictor-corrector method?

(a) Φ^n+1=Φ^n+\(\frac{1}{3}\) [2f(t^n,Φ^n )+f(t^n+1,Φ^n+1*)]Δt

(b) Φ^n+1=Φ^n+\(\frac{1}{2}\) [2f(t^n,Φ^n )+f(t^n+1,Φ^n+1*)]Δt

(c) Φ^n+1=Φ^n+\(\frac{1}{3}\) [f(t^n,Φ^n )+2f(t^n+1,Φ^n+1*)]Δt

(d) Φ^n+1=Φ^n+\(\frac{1}{2}\) [f(t^n,Φ^n )+f(t^n+1,Φ^n+1*)]Δt

The question was posed to me in exam.

I'd like to ask this question from Transient Flows in portion Transient Flows of Computational Fluid Dynamics

Answer 1

The correct choice is (d) Φ^n+1=Φ^n+\(\frac{1}{2}\) [f(t^n,Φ^n )+f(t^n+1,Φ^n+1*)]Δt

Best explanation: The predicted result of the two-level prediction-correction method is corrected using the trapezoidal rule. The trapezoidal rule uses the linear interpolation between two time points. The formula is

Φ^n+1=Φ^n+\(\frac{1}{2}\) [f(t^n,Φ^n )+f(t^n+1,Φ^n+1*)]Δt.