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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

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

backward divided difference http numericalmethods eng usf edu
Backward Divided Differencehttp://numericalmethods.eng.usf.edu
definition
Definition

.

Slope at

y

f(x)

x

http://numericalmethods.eng.usf.edu

backward divided difference1
Backward Divided Difference

http://numericalmethods.eng.usf.edu

example
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

slide6

Example (contd.)

http://numericalmethods.eng.usf.edu

slide7

Example (contd.)

Hence

The exact value of

can be calculated by differentiating

as

http://numericalmethods.eng.usf.edu

slide8

Example (contd.)

The absolute relative true error is

http://numericalmethods.eng.usf.edu

effect of step size
Effect Of Step Size

Value of

Using backward Divided difference method.

http://numericalmethods.eng.usf.edu

effect of step size in backward divided difference method
Effect of Step Size in Backward Divided Difference Method

Initial step size=0.05

http://numericalmethods.eng.usf.edu

effect of step size on approximate error
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
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
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
Effect of Step Size on True Error

Initial step size=0.05

http://numericalmethods.eng.usf.edu

effect of step size on absolute relative true error
Effect of Step Size on Absolute Relative True Error

Initial step size=0.05

http://numericalmethods.eng.usf.edu

additional resources
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

slide17
THE END

http://numericalmethods.eng.usf.edu