Phaser is equipped with a comprehensive collection of algorithms for computing orbits of Difference Equations (MAPs) and Ordinary Differential Equations (ODEs). These algorithms range from the most classical to the most modern, with extensive control settings.
For MAPs, the basic algorithm is Iteration. In addition, a Newton's method for locating fixed and periodic points is provided.
For ODEs, the following algorithms suitable for non-stiff, stiff, or symplectic systems are implemented:
- Classic Explicit: Euler (1), Improved Euler (2), Heun (2), Nystrom (3), Runge-Kutta (4), and Runge-Kutta 3/8 (4);
- Classic Implicit: Implicit Euler (1), Midpoint (2), Trapezoid (2), SDIRK (3), Lobatto (4), Gauss (4), Radau IA (5), and Gauss (6);
- Modern Explicit: Dormand-Prince 5(4), Dormand-Prince 8(5,3), and ODEX;
- Modern Implicit: SEULEX.
In addition to these algorithms, a Newton's method for locating Equilibria of systems of ODEs is provided.2 of 2