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Differentiation and Integration (Integration (Newton-Cotes formula (closed…
Differentiation and Integration
Differentiation
First order derivative
2-point formula
Forward difference
Backward difference
3-point formula
Left end
Mid point
Right end
Second order derivative
Midpoint
Richardson’s extrapolation
(algebra technique to generate higher order result)
Integration
Newton-Cotes formula
closed formula
Trapezoidal rule (n=1)
Simpson's rule (n=2)
Simpson's 3/8 rule (n=3)
open formula
Midpoint (n=0)
Coposite rules
Composite trapezoidal rule
Composite Simpson's rule
Adaptive quadrature
Gaussian quadrature
Algorithm goodness
Robustness (stability)
accuracy (error term, degree of accuracy)