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Python-Numerical-Analysis

Numerical Analysis algorithms/methods in Python.

Current Implementations

Numerical Integration

  • adaptive Newton-Cotes quadrature

Numerical Differentiation

  • Finite Difference Coefficients Calculator
    • Lagrange polynomial method
    • Taylor series method
  • Jacobian, Gradient, and Hessian approximations
  • Richardson Extrapolation

Interpolation

  • Differentiable Vandermonde Polynomial
  • Linear Splines

Boundary-Value Problems

  • Linear Finite Difference Method
  • Nonlinear Finite Difference Method

Initial-Value Problems

  • Scalar/systems of 1st-order ordinary differential equations (ODEs)
    • Runge-Kutta methods
      • Fixed-step or adaptive-step using step-doubling (orders 1 to 8)
      • Runge-Kutta-Fehlberg methods (orders 1 to 8)
    • Linear Multistep methods
      • Adams-Bashforth-Moulton Predictor-Corrector (orders 1 to 5, fixed-step)
  • Direct methods for solving 2nd-order ODEs
    • Problems of the special form $\frac{d^{2}y}{dt^{2}} = f(t,y)$
      • Runge-Kutta-Nystrom methods (work in progress)
    • General second-order ODEs $\frac{d^{2}y}{dt^{2}} = f(t,y,\frac{dy}{dt})$
      • Runge-Kutta-Nystrom-Generalized (RKNG) methods (work in progress)