Numerical Methods

7.

Numerical Differentiation

7.1.

Finite Difference Formulas

7.1.1.

First Derivative Approximations

7.1.1.1.

Forward Difference

7.1.1.2.

Backward Difference

7.1.1.3.

Central Difference

7.1.1.4.

7.1.2.

Higher-Order Derivatives

7.1.2.1.

Second Derivatives

7.1.2.2.

Higher-Order Formulas

7.1.2.3.

Multi-Point Formulas

7.1.3.

Unequally Spaced Data

7.1.3.1.

Lagrange Polynomial Approach

7.1.3.2.

Finite Difference Tables

7.2.

Richardson Extrapolation

7.2.1.

Extrapolation Principle

7.2.2.

Error Reduction

7.2.3.

Implementation Algorithm

7.3.

7.3.1.

Truncation Error

7.3.2.

Round-off Error

7.3.3.

7.3.4.

Optimal Step Size

7.3.5.

Step Size Selection

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8. Numerical Integration