Numerical Analysis algorithms/methods in Python.
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)
- Runge-Kutta methods
- 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)
- Problems of the special form