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Numerical Methods for STEM Undergraduates: Central Divided Difference in Engineering - Example

This resource authored by Dr. Abolfazl Ranjbar-Nouei provides detailed explanations and examples of using central divided difference method in engineering majors. An example demonstrates the calculation of acceleration given velocity data of a rocket. Step sizes and errors are discussed to enhance understanding. Visit the site for comprehensive learning.

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Numerical Methods for STEM Undergraduates: Central Divided Difference in Engineering - Example

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  1. Central Divided Difference Major: All Engineering Majors Author: دکتر ابوالفضل رنجبر نوعی 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. Central 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 central 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 Central Divided Difference difference method. http://numericalmethods.eng.usf.edu

  9. Effect of Step Size in Central 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 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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