Comparison Between Basic Formulas of Forward, Backward, and Centred Finite Difference (FD)
Original function and data points
0.5−0.5−10.20.40.60.81
First Derivative
0.5−0.5−1123−1−2−3
FFD1h1
0.5−0.5−1123−1−2−3
BFD1h1
0.5−0.5−1123−1−2−3
CFD1h2
Second Derivative
0.5−0.5−110−10−20−30−40−50
FFD2h1
0.5−0.5−110−10−20−30−40−50
BFD2h1
0.5−0.5−110−10−20−30−40−50
CFD2h2
Third Derivative
0.5−0.5−1200400600−200−400−600
FFD3h1
0.5−0.5−1200400600−200−400−600
BFD3h1
0.5−0.5−1200400600−200−400−600
CFD3h2
Fourth Derivative
0.5−0.5−150001000015000−5000
FFD4h1
0.5−0.5−150001000015000−5000
BFD4h1
0.5−0.5−150001000015000−5000
CFD4h2