This is a collection of numerical algorithms to solve ordinary and partial differential equation problems.

• Ordinary Differential Equation (ODE) solvers for initial value problem (IVP):
  • Euler’s method
  • Runge Kutta
    • 1st order Runge Kutta
    • 2nd order Runge Kutta
    • 3rd order Runge Kutta
    • 4th order Runge Kutta
    • 5th order Runge Kutta
    • 6th order Runge Kutta
    • 7th order Runge Kutta
    • 8th order Runge Kutta
    • 10th order Runge Kutta
  • Runge-Kutta-Fehlberg (RKF45) (adaptive step-size control)
  • Adams-Bashforth-Moulton predictor-corrector multi-step method
    • 1st order
    • 2nd order
    • 3rd order
    • 4th order
    • 5th order
  • solvers based on Richardson extrapolation
    • Burlisch-Stoer extrapolation
    • semi-implicit extrapolation (suitable for stiff systems)
  • first order system of ODEs
  • conversion from high order ODE to first order ODE system
• Partial Differential Equation (PDE) solvers
  • finite difference methods:
    • elliptic problem:
      • iterative central difference method (for Poisson’s equation)
    • 1D hyperbolic problem:
      • explicit central difference method (for 1D wave equation)
    • 2D hyperbolic problem:
      • explicit central difference method (for 2D wave equation)
    • 1D parabolic problem:
      • Crank-Nicolson method (for 1D heat or diffusion equation)
    • 2D parabolic problem:
      • alternating direction implicit (ADI) method (for 2D heat or diffusion equation)