Methods of Numerical Analysis - Ver 0.1 (python)

Link to Methods of Numerical Analysis

1. Round-Off Error and Computer Arithmetic

• Absolute Value (o)

• Actual Error (o)

• Absolute Error (o)

• Relative Error (0)

2. Solution of Equations in One Variable

• The Bisection Method (o)

• The Fixed-Point Iteration (o)

• The Newton's Method (o)

• The Secant Method (o)

• The Method of False Position (o)

3. Interpolation and Polynomial Approximation

• Data Approximation and Neville's Method (o) --> needs to test and update

• Divided Differences (o) --> needs to test and update

• Hermite Interpolation (o)

4. Numerical Differentiation and Integration

• Three-Point Midpoint Formula (o)

• Three-Point Endpoint Formula (o)

• Five-Point Midpoint Formula (o)

• Five-Point Endpoint Formula (o)

• Composite Simpson's Rule (o)

• Composite Trapezoidal Rule (o)

• Composite Midpoint Rule (progress)

• Romberg Integration (progress)

• Adaptive Quadrature Method (progress)

• Simpson's Double Integral (o)

• Gaussian Double Integral (o) --> needs to test

• Gaussian Triple Integral (progress)

5. Initial-Value Problems for Ordinary Differential Equations

• Euler's Method (o)

• Runge Kutta Method (Order Four) (o)

• Runge Kutta Fehlberg Method (o) --> needs to test more to find accurate outputs.

• Adams Fourth Order Predictor Corrector (o)

• Adams Variable Step Size Predictor Corrector

• Runge Kutta Method for Systems of Differential Equations

6. Direct Methods for Solving Linear Systems

• Gaussian Elimination with Backward Substitution

• Gaussian Elimination with Partial Pivoting

• Gaussian Elimination with Scaled Partial Pivoting

• LU Factorization

• LDL^t Factorization

• Crout Factorization for Tridiagonal Linear Systems