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7/2/2015 http://numericalmethods.eng.usf.edu 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

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

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3 Definition. Slope at f(x) y x

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http://numericalmethods.eng.usf.edu4 Backward Divided Difference

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http://numericalmethods.eng.usf.edu5 Example Example : The velocity of a rocket is given by wheregiven in m/s andis given in seconds. Use backward difference approximation Of the first derivative of to calculate the acceleration at Use a step size of Solution:

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http://numericalmethods.eng.usf.edu6 Example (contd.)

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http://numericalmethods.eng.usf.edu7 Hence The exact value of can be calculated by differentiating as Example (contd.)

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http://numericalmethods.eng.usf.edu8 The absolute relative true error is Example (contd.)

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http://numericalmethods.eng.usf.edu9 Effect Of Step Size Value ofUsing backward Divided difference method.

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http://numericalmethods.eng.usf.edu10 Effect of Step Size in Backward Divided Difference Method Initial step size=0.05

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http://numericalmethods.eng.usf.edu11 Effect of Step Size on Approximate Error Initial step size=0.05

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http://numericalmethods.eng.usf.edu12 Effect of Step Size on Absolute Relative Approximate Error Initial step size=0.05

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http://numericalmethods.eng.usf.edu13 Effect of Step Size on Least Number of Significant Digits Correct Initial step size=0.05

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http://numericalmethods.eng.usf.edu14 Effect of Step Size on True Error Initial step size=0.05

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http://numericalmethods.eng.usf.edu15 Effect of Step Size on Absolute Relative True Error Initial step size=0.05

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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

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

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