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)