Backward Divided Difference

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# Backward Divided Difference - PowerPoint PPT Presentation

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

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 Differencehttp://numericalmethods.eng.usf.edu
Definition

.

Slope at

y

f(x)

x

http://numericalmethods.eng.usf.edu

Backward Divided Difference

http://numericalmethods.eng.usf.edu

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

Example (contd.)

http://numericalmethods.eng.usf.edu

Example (contd.)

Hence

The exact value of

can be calculated by differentiating

as

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Example (contd.)

The absolute relative true error is

http://numericalmethods.eng.usf.edu

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

Initial step size=0.05

http://numericalmethods.eng.usf.edu

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

Initial step size=0.05

http://numericalmethods.eng.usf.edu

Initial step size=0.05

http://numericalmethods.eng.usf.edu

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

Initial step size=0.05

http://numericalmethods.eng.usf.edu