Bulirsch-Stoer Method in Rust

Implementation of the Bulirsch-Stoer method for stepping ordinary differential equations.

The (Gragg-)Bulirsch-Stoer algorithm combines the (modified) midpoint method with Richardson extrapolation to accelerate convergence. It is an explicit method that does not require Jacobians.

This crate's implementation contains simplistic adaptive step size routines with order estimation. Its API is designed to be useful in situations where an ODE is being integrated step by step with a prescribed time step, for example in simulations of electromechanical control systems with a fixed control cycle period. Only time-independent ODEs are supported, but without loss of generality (since the state vector can be augmented with a time variable if needed).

The implementation follows:

• Press, William H. Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, 2007. Ch. 17.3.2.
• Deuflhard, Peter. "Order and stepsize control in extrapolation methods." Numerische Mathematik 41 (1983): 399-422.