範例EX3-1 EXCEL 計算微分近似解 (向前差 / 向後差 / 中央差)

使用EXCEL求微分近似解

向前差 / 向後差 / 中央差

sin	1	0.841471
cos	1	0.540302
h	f(1+h)	f(1)	f(1+h)-f(1)	( f(1+h)-f(1) ) / h	誤差
0.001	0.84201	0.841471	0.000539881	0.53988148	-0.077887046
0.005	0.84416	0.841471	0.002690982	0.538196382	-0.389767786
0.01	0.84683	0.841471	0.00536086	0.536085981	-0.780364031
0.05	0.86742	0.841471	0.025952241	0.519044816	-3.934369688
0.1	0.89121	0.841471	0.049736375	0.497363753	-7.94713494
h	f(1-h)	f(1)	f(1)-f(1-h)	( f(1)-f(1-h) ) / h	誤差
0.001	0.84093	0.841471	0.000540723	0.540722951	0.077853713
0.005	0.83876	0.841471	0.002712019	0.542403728	0.388934454
0.01	0.83603	0.841471	0.005445006	0.544500621	0.777030715
0.05	0.81342	0.841471	0.02805548	0.5611096	3.851046771
0.1	0.78333	0.841471	0.058144075	0.581440752	7.613968234
h	f(1+h)	f(1-h)	f(1+h)-f(1-h)	( f(1+h)-f(1-h) ) / 2h	誤差
0.001	0.84201	0.84093	0.001080604	0.540302216	-1.66667E-05
0.005	0.84416	0.838759	0.005403001	0.540300055	-0.000416666
0.01	0.84683	0.836026	0.010805866	0.540293301	-0.001666658
0.05	0.86742	0.813416	0.054007721	0.540077208	-0.041661459
0.1	0.89121	0.783327	0.10788045	0.539402252	-0.166583353