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Propagation of Errors. Major: All Engineering Majors Authors: Autar Kaw, Matthew Emmons http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Propagation of Errors http://numericalmethods.eng.usf.edu. Propagation of Errors.

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propagation of errors

Propagation of Errors

Major: All Engineering Majors

Authors: Autar Kaw, Matthew Emmons

http://numericalmethods.eng.usf.edu

Transforming Numerical Methods Education for STEM Undergraduates

http://numericalmethods.eng.usf.edu

propagation of errors1
Propagation of Errors

In numerical methods, the calculations are not made with exact numbers. How do these inaccuracies propagate through the calculations?

http://numericalmethods.eng.usf.edu

example 1
Example 1:

Find the bounds for the propagation in adding two numbers. For example if one is calculating X +Y where

X = 1.5 ± 0.05

Y = 3.4 ± 0.04

Solution

Maximum possible value of X = 1.55 and Y = 3.44

Maximum possible value of X + Y = 1.55 + 3.44 = 4.99

Minimum possible value of X = 1.45 and Y = 3.36.

Minimum possible value of X + Y = 1.45 + 3.36 = 4.81

Hence

4.81 ≤ X + Y ≤4.99.

http://numericalmethods.eng.usf.edu

propagation of errors in formulas
Propagation of Errors In Formulas

If

is a function of several variables

then the maximum possible value of the error in is

http://numericalmethods.eng.usf.edu

example 2
Example 2:

The strain in an axial member of a square cross-section is given by

Given

Find the maximum possible error in the measured strain.

http://numericalmethods.eng.usf.edu

slide7

Example 2:

Solution

http://numericalmethods.eng.usf.edu

slide8

Example 2:

Thus

Hence

http://numericalmethods.eng.usf.edu

example 3
Example 3:

Subtraction of numbers that are nearly equal can create unwanted inaccuracies. Using the formula for error propagation, show that this is true.

Solution

Let

Then

So the relative change is

http://numericalmethods.eng.usf.edu

example 31
Example 3:

For example if

= 0.6667

= 66.67%

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/propagation_of_errors.html

slide12
THE END

http://numericalmethods.eng.usf.edu

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