A discrete second derivative is given by f ( x ) 2 f ( x ) 1 ( 1 2 2 ) f ( x 2 ) 1 6 f ( x ) 3 0 f ( x ) 1 6 f ( x ) f ( x 2 ) By way of an appropriate Taylor expansion in , determine the order of accuracy of 2 f ( x )

Question

A discrete second derivative is given by f ( x ) 2 f ( x )   1   ( 1 2   2 )   f ( x   2 )   1 6 f ( x   ) 3 0 f ( x )   1 6 f ( x ) f ( x 2 )     By way of an appropriate Taylor expansion in , determine the order of accuracy of 2 f ( x )

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A discrete second derivative is given by f ( x ) 2 f ( x ) = 1 / ( 1 2 ^ 2 )

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