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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

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This is to build a library for the numerical method in Python.

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