# Ordinary Differential Equations

This chapter describes functions for solving ordinary differential equation (ODE) initial value problems. The library provides a variety of low-level methods, such as Runge-Kutta and Bulirsch-Stoer routines, and higher-level components for adaptive step-size control. The components can be combined by the user to achieve the desired solution, with full access to any intermediate steps.

These functions are declared in the header file ``gsl_odeiv.h'`.

- Defining the ODE System
- Stepping Functions
- Adaptive Step-size Control
- Evolution
- ODE Example programs
- ODE References and Further Reading