Table 2 Central finite difference coefficients for approximating a second derivative in one dimension28

From: Further improving quantum algorithms for nonlinear differential equations via higher-order methods and rescaling

Order k

Coefficients a0 to ak

1

− 2, 1

2

− 5/2, 4/3, − 1/12

3

− 49/18, 3/2, − 3/20, 1/90

4

− 205/72, 8/5, − 1/5, 8/315, − 1/560

5

− 5269/1800, 5/3, − 5/21, 5/126, − 5/1008, 1/3150

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