User documentation

In this section we will present how to use ponio step by step, with tutorials.

Learning ponio by tutorials

• Before starting
  • Installation
  • List of variables available in CMakeLists.txt
• Very first steps with Lorenz system
  • Explicit Runge-Kutta solver
  • Lawson solver
  • Diagonal implicit Runge-Kutta solver
  • Splitting solver
• Understand observers with Lotka-Volterra equations
  • The file observer
  • The cout observer
  • The stream observer
  • The user-defined observer
• Manage your time loop with Curtiss-Hirschfelder equation
  • ponio::solve function
  • A while loop
  • A for loop
• How-to guides
  • How-to: solve a simple ODE
  • How-to: solve an ODE with an implicit method
  • How-to: understand ponio::time_iterator
  • How-to: change tolerances for adaptive time step methods

We provide also a presentation of all kind of algorithms to solve ODE

List of time integrators

• Time integrators
  • Runge-Kutta methods from Butcher tableau
    • Explicit methods
    • Embedded methods
    • Diagonal implicit methods
    • Lawson methods
    • Exponential Runge-Kutta methods
    • Additive Runge-Kutta methods
  • Extended stability methods
    • Runge-Kutta Chebyshev method
    • ROCK2 method
    • ROCK4 method
    • Runge-Kutta Legendre method
  • Splitting methods
    • Lie Splitting method
    • Strang Splitting method
    • Adaptive time step Strang splitting method
  • IMEX methods with extended stability method
  • Bibliography