RKF45 is a FORTRAN77 library which implements the Watt and Shampine RKF45 ODE solver.
The RKF45 ODE solver is a Runge-Kutta-Fehlberg algorithm for solving an ordinary differential equation, with automatic error estimation using rules of order 4 and 5.
RKF45 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.
CWG_ODE, a FORTRAN77 library which implements three ODE solvers by C William Gear.
DRIV, a FORTRAN77 library which solves real or complex systems of ordinary differential equations;
NMS, a FORTRAN77 library which includes the DDRIV package of ODE solvers.
ODE, a FORTRAN77 library which solves a system of ordinary differential equations, by Shampine and Gordon.
ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.
RK4, a FORTRAN77 library which applies the fourth order Runge-Kutta algorithm to estimate the solution of an ordinary differential equation at the next time step.
TEST_ODE, a FORTRAN90 library which contains routines which define some test problems for ODE solvers.
You can go up one level to the FORTRAN77 source codes.