1.

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*)]ΔtThe 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»

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.



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