Central Divided Difference Major All Engineering Majors Authors

Central Divided Difference Major: All Engineering Majors Authors: Autar Kaw, Sri Harsha Garapati http: //numericalmethods. eng. usf. edu Numerical Methods for STEM undergraduates 5/25/2021 http: //numericalmethods. eng. usf. edu 1

Definition . y Slope at f(x) x 2 lmethods. eng. usf. edu ht

Central Divided Difference 3 lmethods. eng. usf. edu ht

Example: The velocity of a rocket is given by where given in m/s and the first derivative of is given in seconds. Use central difference approximation of to calculate the acceleration at Use a step size of Solution: 4 lmethods. eng. usf. edu ht

Example (contd. ) 5 lmethods. eng. usf. edu ht

Example (contd. ) Hence The exact value of can be calculated by differentiating as 6 lmethods. eng. usf. edu ht

Example (contd. ) The absolute relative true error is 7 lmethods. eng. usf. edu ht

Effect Of Step Size Value of 8 Using Central Divided Difference difference method. lmethods. eng. usf. edu ht

Effect of Step Size in Central Divided Difference Method Initial step size=0. 05 9 lmethods. eng. usf. edu ht

Effect of Step Size on Approximate Error Initial step size=0. 05 10 lmethods. eng. usf. edu ht

Effect of Step Size on Absolute Relative Approximate Error Initial step size=0. 05 11 lmethods. eng. usf. edu ht

Effect of Step Size on Least Number of Significant Digits Correct Initial step size=0. 05 12 lmethods. eng. usf. edu ht

Effect of Step Size on True Error Initial step size=0. 05 13 lmethods. eng. usf. edu ht

Effect of Step Size on Absolute Relative True Error Initial step size=0. 05 14 lmethods. eng. usf. edu ht