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The approximation of the derivative taken by the Crank-Nicolson scheme is the same as the __________ of spatial derivative.

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The approximation of the derivative taken by the Crank-Nicolson scheme is the same as the __________ of spatial derivative.

(a) second order forward difference approximation

(b) backward difference approximation

(c) forward difference approximation

(d) central difference approximation

The question was posed to me in unit test.

Question is taken from Transient Flows in chapter Transient Flows of Computational Fluid Dynamics

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Right choice is (d) central difference approximation

Easiest explanation: The central difference scheme of the spatial derivative uses the previous and the next neighbours for the approximation. The Crank-Nicolson scheme also uses such an approximation for its time derivative.

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