Comparison Between Basic and Higher Accuracy Formulas of Backward Finite Difference (FD)
Original function and data points
0.20.40.60.81−0.2−0.4−0.6−0.8−10.20.40.60.81
Basic Formulas Higher Accuracy Formulas
First Derivative
0.20.40.60.81−0.2−0.4−0.6−0.8−1123−1−2−3
BFD1h1
0.20.40.60.81−0.2−0.4−0.6−0.8−1123−1−2−3
BFD1h2
Second Derivative
0.20.40.60.81−0.2−0.4−0.6−0.8−110−10−20−30−40−50
BFD2h1
0.20.40.60.81−0.2−0.4−0.6−0.8−110−10−20−30−40−50
BFD2h2
Third Derivative
0.20.40.60.81−0.2−0.4−0.6−0.8−1200400600−200−400−600
BFD3h1
0.20.40.60.81−0.2−0.4−0.6−0.8−1200400600−200−400−600
BFD3h2
Fourth Derivative
0.20.40.60.81−0.2−0.4−0.6−0.8−150001000015000−5000
BFD4h1
0.20.40.60.81−0.2−0.4−0.6−0.8−150001000015000−5000
BFD4h2