RK4 is a C library which implements a simple Runge-Kutta solver for an initial value problem.
The rk4() function does not include any error estimator. It takes a single step at a time, requiring the user to control the step size.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
RK4 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
GSL, a C++ library which includes routines for solving differential equations.
ODE, a C library which solves a system of ordinary differential equations, by Shampine and Gordon.
ODE_MOSHIER, a C library which implements the Adams-Bashforth-Moulton and Runge-Kutta (RK) methods of solving systems of ordinary differential equations, by Steven Moshier.
ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.
RKF45, a C library which implements the Runge-Kutta-Fehlberg ODE solver.
TEST_ODE, a FORTRAN90 library which contains routines which define some test problems for ODE solvers.
You can go up one level to the C source codes.