Optimized Finite Difference Formulas for Accurate High Frequency Components

Table 2

Largest wavenumbers for which the corresponding error is bound by . These values have been obtained by solving the nonlinear systems shown in Appendix for the optimal weights.

Conventional nodes
	s	0.0843	0.3136	0.5480	0.7481	0.9141	1.0525
	o	0.1338	0.5415	0.9651	1.3121	1.5814	1.7465
	s	0.0236	0.2338	0.4944	0.7204	0.9051	1.0571
	o	0.0332	0.3919	0.8624	1.2582	1.5622	1.7922
	s		0.1561	0.3565	0.5441	0.7061	0.8445
	o		0.2621	0.6236	0.9589	1.2350	1.4586
Staggered nodes
	s	0.1339	0.4644	0.7654	1.0022	1.1889	1.3358
	o	0.2125	0.8011	1.3396	1.7337	2.0120	2.2114
	s	0.0490	0.38301	0.7313	1.0025	1.2112	1.3724
	o	0.0693	0.6404	1.2648	1.7224	2.0368	2.2551
	s	0.0283	0.2559	0.5269	0.7563	0.9427	1.0928
	o	0.0400	0.4282	0.9155	1.3138	1.6136	1.8385