ChE 250 Numeric Methods

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ChE 250 Numeric Methods

• Lecture 3, Chapra Chapter 3
• 20070122

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Outline

• Chapter 3
• Approximations and Round-Off Errors
• Significant Figures
• Accuracy Precision
• Error Definitions
• Round-Off Errors

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Approximations and Round-Off Errors

• Significant Figures
• reliability of a numeric value
• For measurements, it is smallest division one.
• For computers, it is a limitation of the memory
  storage space

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Approximations and Round-Off Errors

• Significant Figures
• Accuracy Precision
• Accuracy how close to the true value
• Precision how computed values agree with each
  other
• For our purposes we will roll these together into
  error

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Approximations and Round-Off Errors

• Significant Figures
• Accuracy Precision
• Error Definitions
• True error
• Not useful in the absence of analytical solution
• Percent relative error
• Used for iterative solutions
• Acceptable error
• Stopping criteria based on n, the number of
  significant figures

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Error for Parachute Example
Analytical Finite Difference Finite Difference True Error Relative Error
t v-analytical t v-numeric
0 0.00 0 0.00
2 16.40 2 19.60 -19.48 100.00
4 27.77 4 32.00 -15.25 38.76
6 35.64 6 39.86 -11.82 19.70
8 41.10 8 44.82 -9.07 11.08
10 44.87 10 47.97 -6.90 6.56
12 47.49 12 49.96 -5.20 3.98
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Approximations and Round-Off Errors

• Significant Figures
• Accuracy Precision
• Error Definitions
• Round-Off Errors
• Intrinsic error associated with binary computing
  using finite memory

8
Preparation for Jan 24th

• Reading
• Chapra Chapter 4 Truncation errors and the
  Taylor Series
• Reminder Homework set 1 due on Wednesday at the
  beginning of class.