Which of these equations give the derivative of the function T at time t as given by the Crank-Nicolson scheme?(a) \(\frac{T(t+\Delta t)-T(t-\Delta t)}{2 \Delta t}\)(b) \(\frac{T(t+\Delta t)+T(t-\Delta t)}{2 \Delta t}\)(c) \(\frac{T(t+\Delta t)-T(t-\Delta t)}{\Delta t}\)(d) \(\frac{T(t+\Delta t)+T(t-\Delta t)}{\Delta t}\)This question was addressed to me during an interview for a job.The query is from Transient Flows topic in division Transient Flows of Computational Fluid Dynamics

Which of these equations give the derivative of the function T at time

1.	Which of these equations give the derivative of the function T at time t as given by the Crank-Nicolson scheme?(a) \(\frac{T(t+\Delta t)-T(t-\Delta t)}{2 \Delta t}\)(b) \(\frac{T(t+\Delta t)+T(t-\Delta t)}{2 \Delta t}\)(c) \(\frac{T(t+\Delta t)-T(t-\Delta t)}{\Delta t}\)(d) \(\frac{T(t+\Delta t)+T(t-\Delta t)}{\Delta t}\)This question was addressed to me during an interview for a job.The query is from Transient Flows topic in division Transient Flows of Computational Fluid Dynamics
Answer» The CORRECT choice is (a) \(\frac{T(t+\DELTA t)-T(t-\Delta t)}{2 \Delta t}\) To explain: The Crank-Nicolson scheme uses the previous and the NEXT steps to get the DERIVATIVE at the current step. EXPRESSING it mathematically, \(\frac{\partial T(t)}{\partial t} = \frac{T(t+\Delta t)-T(t-\Delta t)}{2 \Delta t}\).

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