Optimized Finite Difference Formulas for Accurate High Frequency Components

Table 3

Optimized weights for second derivative and using (18)–(20).

standard	0.1855	0.4573	0.7039	0.9073	1.0736	1.2110
opt. (see (20))	0.1855	0.7801	1.2294	1.5813	1.8449	2.0442
opt. (see (21))	0.3120	0.8057	1.2500	1.5954	1.8550	2.0508
	−2	−2.556451	−2.824639	−2.978478	−3.071991	−3.131331
	1	1.371592	1.579082	1.708933	1.792168	1.846830
		−0.093366	−0.184639	−0.261022	−0.319217	−0.361654
			0.017876	0.046789	0.077604	0.104965
				−0.005460	−0.016873	−0.030957
					0.002313	0.007709
						−0.001228