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Backward Divided Difference

Backward Divided Difference. Major: All Engineering Majors Authors: Autar Kaw, Sri Harsha Garapati http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Backward Divided Difference http://numericalmethods.eng.usf.edu. Definition. . .

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Backward Divided Difference

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

  2. Backward Divided Differencehttp://numericalmethods.eng.usf.edu

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

  4. Backward Divided Difference http://numericalmethods.eng.usf.edu

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

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

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

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

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

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

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

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

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

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

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

  16. Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit http://numericalmethods.eng.usf.edu/topics/continuous_02dif.html

  17. THE END http://numericalmethods.eng.usf.edu

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