Scientific Computing in Python

• Analysis

  • Quadrature
    • Midpoint rule
    • Trapezoidal rule
    • Simpson rule
    • Gauss Legendre, including Golub-Welsch
    • All Rules in arbitrary dimensions
  • ODEs
    • Explicit euler
    • Implicit euler
    • Implicit midpoint
    • Implicit trapezoidal
    • Velocity verlet
    • Taylor methods of arbitrary order
    • Arbitrary Rungekutta methods
    • Collocation points to Butcher tableau
    • Splitting methods
    • Rosebrock-Wanner 23 adaptive method
    • Exponential euler
    • Krylov-Subspace solver for linear ODEs
  • Solving Equations
    • Secant
    • Newton
    • Broyden

• Linear Algebra

  • QR-Decomposition
    • Householder
    • Givens
    • Gram-Schmidt
    • Modified Gram-Schmidt
  • Cholesky-Decomposition
  • Eingenvalue/vector calculation
    • QR-Iteration
    • Power methods
  • Least Squares
    • Linear via QR, SVD or normal form
    • Total linear lstsq via SVD
    • Newton
    • Gauss-Newton