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Numerical Differentiation
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Basic Method
- n = 2
- Lagrange Polynomial
- Taylar Series
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Better approximation
- n = 3, 4, ...
- Taylar Series
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Richardson's Extrapolation
- is used to generate high-accuracy results while using low-order formula
- higher-order derivative exist
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Numerical Integration
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Basic Method
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Trapezoidal rule
- Lagrange Polynomial
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Midpoint rule
- Taylar Series
- Simpson's rule
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Newton-Cotes formula
- n is odd
- n is even
- n = 0 -> Midpoint rule(open)
- n = 1 -> Trapezoidal rule(closed)
- n = 2 -> Simpson's rule(closed)
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Composite Numerical Integration
- Composite Simpson's rule
- Composite Trapezoidal rule
- Composite Midpoint rule
- Romberg Integration
- Gaussian Quadrature