Forward Divided Difference Major: All Engineering Majors Authors: Autar Kaw, Sri Harsha Garapati http://numericalmethods.eng.usf.edu Numerical Methods for STEM undergraduates 2/24/2019 http://numericalmethods.eng.usf.edu

Definition . y Slope at f(x) x http://numericalmethods.eng.usf.edu

Forward Divided Difference http://numericalmethods.eng.usf.edu

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

Example (contd.) http://numericalmethods.eng.usf.edu

Example (contd.) Hence The exact value of can be calculated by differentiating as http://numericalmethods.eng.usf.edu

Example (contd.) The absolute relative true error is http://numericalmethods.eng.usf.edu

Effect Of Step Size Value of Using forward difference method. http://numericalmethods.eng.usf.edu

Effect of Step Size in Forward Divided Difference Method Initial step size=0.05 http://numericalmethods.eng.usf.edu

Effect of Step Size on Approximate Error Initial step size=0.05 http://numericalmethods.eng.usf.edu

Effect of Step Size on Absolute Relative Approximate Error Initial step size=0.05 http://numericalmethods.eng.usf.edu

Effect of Step Size on Least Number of Significant Digits Correct Initial step size=0.05 http://numericalmethods.eng.usf.edu

Effect of Step Size on True Error Initial step size=0.05 Initial step size=0.05 http://numericalmethods.eng.usf.edu

Effect of Step Size on Absolute Relative True Error Initial step size=0.05 http://numericalmethods.eng.usf.edu