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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)