13 Ordinary Differential Equations
Stan provides a built-in mechanism for specifying and solving systems of ordinary differential equations (ODEs). Stan provides three different integrators, tuned for solving non-stiff systems and for stiff systems.
For a discussion of stiff ODE systems, see the stiff ODE section. In a nutshell, the stiff solvers are slower, but more robust; how much so depends on the system and the region of parameter space. The function signatures for Stan’s ODE solvers can be found in the reference manual section on ODE solvers.
Dormand, John R, and Peter J Prince. 1980. “A Family of Embedded Runge-Kutta Formulae.” Journal of Computational and Applied Mathematics 6 (1): 19–26.
Ahnert, Karsten, and Mario Mulansky. 2011. “Odeint—Solving Ordinary Differential Equations in C++.” arXiv 1110.3397.
Cohen, Scott D, and Alan C Hindmarsh. 1996. “CVODE, a Stiff/Nonstiff ODE Solver in C.” Computers in Physics 10 (2): 138–43.
Serban, Radu, and Alan C Hindmarsh. 2005. “CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS.” In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 257–69. American Society of Mechanical Engineers.