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Forward Divided Difference

This resource explores the Forward Divided Difference method, a numerical approach essential for engineering majors to approximate derivatives. It provides a comprehensive guide on using this method to calculate acceleration from velocity data, alongside practical examples highlighting the significance of step size in determining accuracy and error. The study also delves into the effects of varying step sizes on approximate errors and significant digits, enabling students to grasp the implications of numerical methods in engineering contexts.

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Forward Divided Difference

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

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

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

  4. Example Example: 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

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

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

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

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

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

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

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

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

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

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

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