1. SE301: Numerical Methods Topic 6 Numerical Differentiation Lecture 23
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Read Chapter 23, Sections 1-2
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2. Lecture 23 Numerical Differentiation
First order derivatives
High order derivatives
Richardson Extrapolation
Examples
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3. Motivation How do you evaluate the derivative of a tabulated function.
How do we determine the velocity and acceleration from tabulated measurements.
Time
(second)
Displacement
(meters)
30.1 5
48.2 10
50.0 15
40.2
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4. Recall
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5. Three Formulas
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6. The Three Formulas
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7. Forward/Backward Difference Formula
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8. Central Difference Formula
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9. The Three Formulas (Revisited)
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10. Higher Order Formulas
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11. Other Higher Order Formulas
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12. Richardson Extrapolation
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13. Richardson Extrapolation
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14. Richardson Extrapolation Table
D(0,0)=Φ(h)
D(1,0)=Φ(h/2)
D(1,1)
D(2,0)=Φ(h/4)
D(2,1)
D(2,2)
D(3,0)=Φ(h/8)
D(3,1)
D(3,2)
D(3,3)
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15. Richardson Extrapolation Table
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16. Example
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17. Example First Column
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18. Example Richardson Table
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19. Example Richardson Table
This is the best estimate of the derivative of the function.
All entries of the Richardson table are estimates of the derivative of the function.
The first column are estimates using the central difference formula with different h.
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